Lawyers ramped up their fight over how to manage the 23andMe Inc. data breach litigation, disagreeing on everything from whether to immediately settle the cases to handling class members who are “truly frightened.”

Various teams of lawyers have applied for leadership of three dozen data breach lawsuits coordinated in multidistrict litigation this month before U.S. District Judge Edward Chen in the Northern District of California. Chen, in a Tuesday order, instructed lawyers to “propose a slate of counsel from different firms.” He set a May 30 hearing for appointing lead counsel.