On Appeal from the United States District Court for the Southern District of New York Ordinarily, defendants are deemed to have waived or forfeited defenses that they did not raise at the outset of the litigation. But defenses based on subject-matter jurisdiction — the courts’ statutory or constitutional power to adjudicate the case — are nonwaivable. Defendants can raise such defenses at any stage in the litigation. Presidential immunity is a defense that entitles the President to absolute immunity from damages liability for acts within the outer perimeter of his official responsibilities. This case presents a vexing question of first impression: whether presidential immunity is waivable. We answer in the affirmative and further hold that Donald J. Trump (“Defendant”) waived the defense of presidential immunity by failing to raise it as an affirmative defense in his answer to E. Jean Carroll’s (“Plaintiff’s”) complaint, which alleged that Defendant defamed her by claiming that she had fabricated her account of Defendant sexually assaulting her in the mid-1990s. Accordingly, we AFFIRM the July 5, 2023 order of the United States District Court for the Southern District of New York (Lewis A. Kaplan, Judge) denying Defendant’s motion for summary judgment insofar as it rejected Defendant’s presidential immunity defense and denied his request for leave to amend his answer to add presidential immunity as a defense. We likewise AFFIRM the District Court’s August 7, 2023 order insofar as it struck Defendant’s presidential immunity defense from his answer to Plaintiff’s amended complaint. We DISMISS for lack of appellate jurisdiction the appeal of the District Court’s July 5, 2023 order insofar as it determined that Defendant’s statements about Plaintiff were defamatory per se. Finally, we REMAND the case to the District Court for further proceedings consistent with this opinion. JOSE CABRANES, C.J. Ordinarily, defendants are deemed to have waived or forfeited defenses that they did not raise at the outset of the litigation.1 But defenses based on subject-matter jurisdiction — “the courts’ statutory or constitutional power to adjudicate the case”2 — are nonwaivable. Defendants can raise such defenses “at any stage in the litigation.”3 Presidential immunity is a defense that stems from “the President’s unique office, rooted in the constitutional tradition of the separation of powers and supported by our history,” and entitles the President to “absolute…immunity from damages liability for acts within the outer perimeter of his official responsibilities.”4 For example, the Supreme Court held in Nixon v. Fitzgerald that presidential immunity protected former President Richard Nixon from a lawsuit by an ex-Air Force employee who alleged that Nixon fired him in retaliation for testifying before Congress about cost overruns.5 Conversely, the Court held in Clinton v. Jones that presidential immunity did not shield President Clinton from civil liability for actions allegedly taken when he was Governor of Arkansas because they were not official presidential acts.6 This case presents a vexing question of first impression: whether presidential immunity is waivable. We answer in the affirmative and further hold that Donald J. Trump (“Defendant”) waived the defense of presidential immunity by failing to raise it as an affirmative defense in his answer to E. Jean Carroll’s (“Plaintiff’s”) complaint, which alleged that Defendant defamed her by claiming that she had fabricated her account of Defendant sexually assaulting her in the mid-1990s. Accordingly, we AFFIRM the July 5, 2023 order of the United States District Court for the Southern District of New York (Lewis A. Kaplan, Judge) denying Defendant’s motion for summary judgment insofar as it rejected Defendant’s presidential immunity defense and denied his request for leave to amend his answer to add presidential immunity as a defense. We likewise AFFIRM the District Court’s August 7, 2023 order insofar as it struck Defendant’s presidential immunity defense from his answer to Plaintiff’s amended complaint. We DISMISS for lack of appellate jurisdiction the appeal of the District Court’s July 5, 2023 order insofar as it determined that Defendant’s statements about Plaintiff were defamatory per se. Finally, we REMAND the case to the District Court for further proceedings consistent with this opinion. I. BACKGROUND The relevant facts in this appeal are undisputed. We summarize them below. A. Factual Background On June 21, 2019, Plaintiff publicly accused Defendant of sexually assaulting her in the mid-1990s.7 Defendant, who was President of the United States at the time of the accusations, denied Plaintiff’s claims in a series of public statements. In the first, released that same day, he claimed that “it never happened,” he “never met” Plaintiff, and that “[s]he is trying to sell a new book — that should indicate her motivation.”8 The next day, he stated that “[t]his is a woman who has also accused other men of things…It is a totally false accusation.”9 On November 4, 2019, Plaintiff responded by suing Defendant for defamation in New York State Supreme Court. Defendant filed his answer on January 23, 2020. On September 8, 2020, the United States removed the case to the United States District Court for the Southern District of New York pursuant to the Westfall Act.10 B. Procedural Background On December 22, 2022, Defendant moved for summary judgment.11 In his reply brief, filed on January 19, 2023, he raised for the first time the argument that presidential immunity barred liability. On July 5, 2023, the District Court denied Defendant’s motion for summary judgment after determining that Defendant waived presidential immunity and denied Defendant’s request for leave to amend his answer to add presidential immunity as a defense (“July 5 Order”).12 The Court denied Defendant’s request for leave to amend on two independent grounds: first, that the request was futile, and second, that Defendant unduly delayed in raising the defense and granting the request would prejudice Plaintiff.13 The Court also rejected Defendant’s argument that his statements were not defamatory per se.14 Defendant appealed the July 5 Order on July 19, 2023. Meanwhile, on May 22, 2023, Plaintiff filed an amended complaint that added, inter alia, more statements by Defendant alleging that Plaintiff’s accusations were false and politically motivated. Defendant filed his answer to Plaintiff’s amended complaint on June 27, 2023. The amended answer for the first time raised presidential immunity as an affirmative defense. On August 7, 2023, the District Court struck Defendant’s presidential immunity defense from his amended answer on the ground that it had been waived and, even if not, “would have been insufficient as a defense” (“August 7 Order”).15 On August 10, 2023, Defendant appealed the August 7 Order. Defendant sought a stay from the District Court, arguing that his appeal of the District Court’s July 5 Order, which rejected Defendant’s presidential immunity defense, divested the District Court of jurisdiction. On August 18, 2023, the District Court denied Defendant’s stay motion upon determining his appeal to be frivolous.16 Defendant then sought an emergency stay from our Court, which a motions panel denied on September 13, 2023. The same day, the motions panel ordered the consolidation of Defendant’s appeals of the July 5 Order and the August 7 Order and set an expedited briefing schedule. II. DISCUSSION This case concerns appeals from two related orders by the District Court. The July 5 Order denied Defendant’s motion for summary judgment on the ground that Defendant waived his presidential immunity defense and further denied Defendant’s request for leave to amend his answer to add presidential immunity as an affirmative defense. The August 7 Order struck Defendant’s affirmative defense of presidential immunity from his answer to Plaintiff’s amended complaint on the ground that Defendant had already waived this defense. We hold that presidential immunity is waivable and that Defendant waived this defense.17 Thus, the District Court did not err in its order denying Defendant’s motion for summary judgment, nor did it err, much less “abuse its discretion,” in denying his belated request for leave to amend his answer to add presidential immunity as a defense.18 We also hold that the District Court did not err in striking Defendant’s presidential immunity defense from his answer to Plaintiff’s amended complaint.19 Nor did the District Court err in retaining jurisdiction after Defendant filed his notice of appeal on July 19, 2023.20 Finally, we hold that we lack appellate jurisdiction to consider whether Defendant’s statements were defamatory per se.21 A. Whether Defendant Waived Presidential Immunity22 Is presidential immunity waivable? And if so, did Defendant waive it? The answer to both questions is yes. 1. Whether Presidential Immunity Is Waivable Defendant argues that presidential immunity is a jurisdictional defense and is thus nonwaivable.23 We disagree. The Supreme Court recognized in Nevada v. Hicks that “[t]here is no authority whatever for the proposition that absolute-and qualified-immunity defenses pertain to the court’s jurisdiction.”24 And we have repeatedly distinguished absolute immunity defenses from defenses based on subject-matter jurisdiction.25 Rather than acknowledge Hicks or our precedents, Defendant points to scattered references to “jurisdiction” in Supreme Court cases involving presidential immunity.26 But as we have recently been reminded by the Supreme Court, “[t]he mere fact that [the Supreme] Court previously described something without elaboration as jurisdictional…does not end the inquiry.”27 We must ask if the prior decision addressed whether the provision or defense is “‘technically jurisdictional’ — whether it truly operates as a limit on a court’s subjectmatter jurisdiction — and whether anything in the decision ‘turn[ed] on that characterization.’”28 Accordingly, “[i]f a decision simply states that ‘the court is dismissing “for lack of jurisdiction” when some threshold fact has not been established,’ it is understood as a ‘drive-by jurisdictional ruling’ that receives no precedential effect.”29 None of the cases on which Defendant relies indicate that presidential immunity is jurisdictional — indeed, quite the opposite. Defendant relies primarily on the following passage in Nixon: [A] court, before exercising jurisdiction, must balance the constitutional weight of the interest to be served against the dangers of intrusion on the authority and functions of the Executive Branch. When judicial action is needed to serve broad public interests…the exercise of jurisdiction has been held warranted. In the case of this merely private suit for damages based on a President’s official acts, we hold it is not.30 But Nixon hurts, not helps, Defendant’s case. The passage quoted above follows a threshold analysis of whether the Supreme Court had subject-matter jurisdiction over the dispute.31 Pursuant to the usual practice in the federal courts,32 only once assured of its subject-matter jurisdiction did the Supreme Court proceed to the “merits” — i.e., to whether the President was entitled to immunity.33 Nor do the passing references to “jurisdiction” in Mississippi v. Johnson or in Clinton v. Jones support Defendant’s position. In Johnson, the question was whether a state could obtain an injunction to prevent the President from carrying out an Act of Congress, not whether a President is liable for damages in a private civil suit.34 And like Nixon, Clinton first held that the Supreme Court had subject-matter jurisdiction before proceeding to the immunity question.35 Neither Nixon nor Clinton addressed whether presidential immunity is “technically jurisdictional,” nor did “anything in the decision[s] turn[] on that characterization.”36 Thus, Clinton’s reference to “jurisdiction” — the Court’s determination that “[t]he Federal District Court has jurisdiction to decide this case”37 — is, like Nixon’s, best characterized as a “drive-by jurisdictional ruling” that “should be accorded no precedential effect” because it ultimately does not bear on the question of whether presidential immunity is jurisdictional.38 All in all, Defendant provides no case that turns on whether presidential immunity is jurisdictional, much less one holding that it is jurisdictional, and Nixon — described by Defendant’s counsel at oral argument as the “main case” and “the only binding precedent” on presidential immunity — points in the opposite direction.39 Next, Defendant contends that “the separation-of-powers doctrine” renders presidential immunity nonwaivable because “an impermissible inter-branch conflict will always arise when a court seeks to impute civil liability on a President for the performance of his official acts.”40 But separation-of-powers considerations militate in favor of, not against, recognizing presidential immunity as waivable. A President’s autonomy should be protected; thus, a President should be able to litigate if he chooses to do so. Indeed, at least one President has declined to invoke presidential immunity, opting instead to settle two civil suits out of court.41 Recognizing presidential immunity as a jurisdictional defense would, the District Court observed, “risk encroachment by the judiciary into the president’s domain by eliminating the president’s ability to choose” whether to litigate.42 Moreover, avoiding undue judicial intrusion on the executive branch undergirds the doctrines of both prosecutorial immunity and presidential immunity. That said, Defendant does not dispute that prosecutorial immunity is waivable. Rather, he argues that the President’s unique constitutional role distinguishes presidential immunity from other forms of absolute immunity such as prosecutorial immunity and judicial immunity.43 But as Defendant acknowledges,44 the Supreme Court has made clear that absolute immunity for prosecutors and judges, on the one hand, and presidential immunity on the other, are closely related. “As is the case with prosecutors and judges,” the Court stated in Nixon, “a President must concern himself with matters likely to ‘arouse the most intense feelings.’”45 And the Court has recently reinforced the “careful analogy” it drew in Nixon, reasoning that “a President, like [judges and prosecutors], must…not be made ‘unduly cautious in the discharge of [his official] duties’ by the prospect of civil liability for official acts.”46 Nor do the Court’s references in Nixon and Harlow v. Fitzgerald — Nixon’s companion case — to the President’s unique status in comparison with other Government officials support Defendant’s position.47 Those passages contrasted the President to other executive officials — such as presidential aides and Cabinet officers — to conclude that, unlike the qualified immunity of these lower-level executive officials, presidential immunity is absolute.48 And although the Supreme Court in Nixon recalled the “special solicitude due to claims alleging a threatened breach of essential Presidential prerogatives under the separation of powers,” the passage in question concerned not whether presidential immunity was waivable, but whether the district court’s order rejecting Nixon’s immunity defense was a “serious and unsettled” question that could be raised on interlocutory appeal.49 Finally, Defendant argues that Article III of the Constitution, which vests judicial power in the federal courts, makes presidential immunity nonwaivable. He reasons as follows. First, violations of Article III — for example, the improper exercise of federal judicial power by a non-Article III entity — are not waivable. Next, separation-of-powers considerations inform both Article III and presidential immunity. Thus, presidential immunity is not waivable. But apart from Nixon (discussed above), none of the cases Defendant draws to our attention concern immunity at all, much less presidential immunity.50 More to the point, it is not accurate to assert that separation-of-powers defenses or arguments are ipso facto nonwaivable.51 To summarize: notwithstanding scattered references to “jurisdiction” in some presidential immunity cases, the Supreme Court has indicated that immunity defenses are not jurisdictional, and that presidential immunity is to be treated like other forms of immunity that Defendant does not dispute are waivable. Moreover, Nixon — the leading presidential immunity case — treats presidential immunity as nonjurisdictional. Finally, recognizing presidential immunity as waivable reinforces, not undermines, the separation of powers and the President’s decisionmaking authority by affording the President an opportunity to litigate if he so chooses. Accordingly, we hold that presidential immunity is waivable. 2. Whether Defendant Waived Presidential Immunity Having determined that presidential immunity is waivable, we reach the question: Did Defendant waive his presidential immunity defense? We hold that he did. Defendant filed his answer to Plaintiff’s original complaint in New York state court in January 2020. But the answer did not invoke presidential immunity. The District Court thus determined that Defendant had waived this defense, a holding Defendant does not challenge in this appeal.52 Indeed, Defendant’s counsel conceded at oral argument that assuming the defense of presidential immunity is waivable, Defendant had waived that defense.53 Accordingly, the District Court did not err in denying Defendant’s motion for summary judgment on the ground that he had waived his presidential immunity defense. We turn next to whether the District Court correctly rejected his attempt to revive it — first in his request for leave to amend his answer, then in his answer to Plaintiff’s amended complaint. B. Defendant’s Request for Leave to Amend “We review a district court’s denial of leave to amend for abuse of discretion, unless the denial was based on an interpretation of law, such as futility, in which case we review the legal conclusion de novo.”54 The District Court did not err, much less “abuse its discretion,”55 when it denied Defendant’s request for leave to amend his answer to add the defense of presidential immunity on grounds of undue delay and prejudice.56 First, Defendant unduly delayed in raising presidential immunity as a defense.57 Three years passed between Defendant’s answer and his request for leave to amend his answer. A three-year delay is more than enough, under our precedents, to qualify as “undue.”58 And Defendant’s excuse for not timely raising the defense — that the question of whether the Westfall Act immunized Defendant was pending before the District Court, this Court, and the District of Columbia Court of Appeals between September 2020 and June 2023 — is unpersuasive.59 Defendant does not explain how the Westfall Act dispute precluded him from raising a defense of presidential immunity. Indeed, Defendant first raised presidential immunity in January 2023 — that is, during the pendency of the Westfall Act dispute. We next conclude that Defendant’s delay unduly prejudiced Plaintiff. “Prejudice,” like “abuse of discretion,” is a legal term of art.60 In gauging whether a proposed amendment would prejudice a party, “we consider, among other factors, whether an amendment would require the opponent to expend significant additional resources to conduct discovery and prepare for trial or significantly delay the resolution of the dispute.”61 Although “mere delay, absent a showing of bad faith or undue prejudice, does not provide a basis for a district court to deny the right to amend,” “the longer the period of an unexplained delay, the less will be required of the nonmoving party in terms of a showing of prejudice.”62 Finally, requests to amend that come at a late stage of the litigation, after discovery has closed and a motion for summary judgment has been filed, are more likely to be prejudicial.63 Had Defendant raised presidential immunity before discovery closed, Plaintiff claims, she would have engaged in discovery on whether Defendant’s actions fell within his official duties.64 First, Plaintiff would have asked Defendant for more detail on the process through which he issued and prepared the June 2019 statements, including how the process compared to his pre-and post-presidential processes.65 Second, Plaintiff would have sought third-party discovery from White House personnel allegedly involved in preparing and issuing the statements.66 Third, Plaintiff would have sought expert testimony from former White House officials and requested internal White House documents from the National Archives regarding former presidents’ processes for issuing statements denying wrongdoing.67 Plaintiff’s counsel represents that they avoided doing so because “the risk of prolonging the litigation and creating complex executive privilege fights did not seem worth it to us, as measured against the absence of an absolute immunity defense, which Mr. Trump had not raised.”68 Against all this, Defendant contends that the discovery Plaintiff would have pursued regarding presidential immunity (whether the statements fell within the President’s official duties) was already explored by Plaintiff in the discovery she pursued regarding the Westfall Act (whether the statements fell within the President’s scope of employment).69 But as counsel for Defendant concedes, the two tests are different.70 The Westfall Act’s scope-of-employment test is subjective, while presidential immunity’s official-duties test is objective.71 And Defendant has no response to Plaintiff’s contention that Defendant’s failure to timely raise presidential immunity informed her decision not to engage in discovery on whether Defendant’s actions fell within his official duties. In sum, three years passed before Defendant raised the defense of presidential immunity, significant additional resources to conduct discovery would be required were Defendant to amend his answer, and the request arose at a late stage of litigation — after discovery closed and Defendant moved for summary judgment. Under these circumstances, we hold that the District Court did not “abuse its discretion” in denying Defendant’s request for leave to amend his answer on grounds of undue delay and prejudice. C. Defendant’s Answer to Plaintiff’s Amended Complaint After the District Court denied Defendant’s request for leave to amend his answer, Plaintiff filed an amended complaint. In response, Defendant filed an answer to the amended complaint asserting presidential immunity. The District Court struck Defendant’s presidential immunity defense from his amended answer, reasoning that “[t]here is nothing new in the amended complaint that would make Mr. Trump’s presidential immunity defense any more viable or persuasive now than it would have been before.”72 We review a district court decision striking an affirmative defense de novo.73 Although “an amended complaint ordinarily supersedes the original, and renders it of no legal effect,” an amended complaint “does not automatically revive all of the defenses and objections that a defendant has waived in response to the original complaint.”74 Defenses that “involve[] the core issue of a party’s willingness to submit a dispute to judicial resolution,” such as lack of personal jurisdiction, improper venue, insufficiency of process, insufficiency of service, or the existence of an arbitration agreement, are “not automatically revived by the submission of an amended complaint” if initially waived.75 To revive such claims, a party “must show that the amended complaint contains charges that, in fairness, should nullify its earlier waiver and allow it to reassess its strategy.”76 Presidential immunity involves the party’s willingness to submit the dispute to judicial resolution and is distinguishable from revivable, merits-based defenses.77 Indeed, the only reason we have jurisdiction over this appeal is that the denial of presidential immunity is a collateral order, a requirement of which is that the issue on appeal be “completely separate from the merits of the action.”78 What’s more, Defendant does not identify any changes to the complaint “that, in fairness, should nullify [his] earlier waiver and allow [him] to reassess [his] strategy.”79 Accordingly, in the unusual circumstances presented here, we hold that the District Court did not err in striking presidential immunity as an affirmative defense from Defendant’s answer to Plaintiff’s amended complaint. D. Whether the District Court Retained Jurisdiction After Defendant Appealed “The filing of a notice of appeal ordinarily divests the district court of jurisdiction over issues decided in the order being appealed.”80 We have previously noted that “[t]he divestiture of jurisdiction rule is, however, not a per se rule. It is a judicially crafted rule rooted in the interest of judicial economy, designed to avoid confusion or waste of time resulting from having the same issues before two courts at the same time. Hence, its application is guided by concerns of efficiency and is not automatic.”81 For example, district courts may retain jurisdiction notwithstanding appeal if the appeal is frivolous.82 The District Court determined that it retained jurisdiction because Defendant’s appeal was frivolous. We need not decide whether Defendant’s appeal is frivolous, for we conclude that under the singular circumstances presented here, considerations of judicial economy and efficiency favor the District Court’s retention of jurisdiction. To hold otherwise would require the District Court on remand to possibly undertake the rather pointless exercise of readopting the orders it has issued since July 19, 2023, the date Defendant appealed the July 7 Order.83 “[O]ur application of the divestiture rule must be faithful to the principle of judicial economy from which it springs,”84 and “it should not be employed to defeat its purposes or to induce endless paper shuffling.”85 This Court has declined to apply the divestiture rule under similar circumstances in the past, and we reach the same result here.86 E. Whether We May Consider Whether Defendant’s Statements Were Defamatory Per Se Apart from appeals taken under the collateral order doctrine,87 orders denying summary judgment are, in general, not immediately appealable.88 And collateral-order doctrine appeals — such as Defendant’s appeals of the July 5 Order and the August 7 Order — do not render other aspects of the case immediately reviewable unless they are “inextricably intertwined” or “necessary to ensure meaningful review” of the collateral orders.89 Defendant argues that none of his statements about Plaintiff were defamatory per se under New York law because they did not tend to cause injury to her trade, business, or profession, and that the District Court applied the wrong legal standard to his statements.90 Far from being inextricably intertwined with or necessary to ensure meaningful review of the District Court’s denial of presidential immunity, whether Defendant’s statements fell within the outer perimeter of his official presidential duties has nothing to do with whether the statements qualify as defamatory per se. Because we have no appellate jurisdiction over the District Court’s determination that Defendant’s statements were defamatory per se, we do not consider Defendant’s argument that the District Court erred in this respect. III. CONCLUSION To summarize, we hold that: (1) Presidential immunity is a waivable defense. (2) Defendant waived the defense of presidential immunity by failing to raise it as an affirmative defense in his answer. (3) The District Court did not err in denying Defendant’s motion for summary judgment insofar as it rejected Defendant’s presidential immunity defense on the ground that he had waived this defense. (4) Defendant unduly delayed in raising presidential immunity as a defense, and permitting Defendant to amend his answer to add the defense would unduly prejudice Plaintiff. Thus, the District Court did not err, much less “abuse its discretion,” in denying Defendant’s request for leave to amend his answer to add presidential immunity as a defense. (5) Presidential immunity is not a defense that is automatically revived by the submission of an amended complaint if initially waived. Thus, the District Court did not err in striking Defendant’s presidential immunity defense from his answer to Plaintiff’s amended complaint. (6) Under the singular circumstances presented here, considerations of judicial economy and efficiency favor the District Court’s retention of jurisdiction after Defendant’s notice of appeal was filed on July 19, 2023. Thus, the District Court did not err in retaining jurisdiction after July 19, 2023. (7) Whether Defendant’s statements about Plaintiff were defamatory per se is neither inextricably intertwined with nor necessary to ensure meaningful review of the District Court’s denial of presidential immunity. Thus, we lack appellate jurisdiction to consider whether Defendant’s statements about Plaintiff were defamatory per se. Accordingly, we AFFIRM the July 5, 2023 order of the District Court denying Defendant’s motion for summary judgment insofar as it rejected Defendant’s presidential immunity defense and denied his request for leave to amend his answer to add presidential immunity as a defense. We likewise AFFIRM the District Court’s August 7, 2023 order insofar as it struck Defendant’s presidential immunity defense from his answer to Plaintiff’s amended complaint. We DISMISS for lack of appellate jurisdiction the appeal of the District Court’s July 5, 2023 order insofar as it determined that Defendant’s statements about Plaintiff were defamatory per se. Finally, we REMAND the case to the District Court for further proceedings consistent with this opinion.