When it comes to disputes over the ownership of artwork that changed hands during the Nazi era, it's hard not to sympathize with the plaintiffs—descendants of Jews who were persecuted or slaughtered during the Holocaust.

But a case pending in the Southern District of New York tests just how far these claims can go.

At issue: a breathtaking Picasso painting, “The Actor,” valued at $150 million that's been owned by the Metropolitan Museum of Art since 1952.