The lawsuit is an outgrowth of an acrimonious split between the Nederlander Organization, which is one of the biggest theater owners in the country, and Ms. Hays, who has parlayed a huge real estate fortune into a successful theater career. The Nederlander and Shorenstein families had jointly run the three big San Francisco theaters for decades — their joint venture was called SHN, for Shorenstein Hays Nederlander — but separated in 2014, and have been in litigation since.

The latest complaint was filed in the Court of Chancery in Delaware, which often handles corporate disputes.

This summer, that same court issued a detailed ruling in a case in which Nederlander accused Ms. Hays of breaking a promise to continue renting the Curran to SHN. In the ruling, the court said “there was no enforceable promise” to that effect, but was also critical of Ms. Hays, saying that she and her husband had breached their fiduciary duties to SHN, and that she “willfully partook in bad faith litigation tactics” during a head-spinning deposition. (Asked how many times she had met with her lawyer to prepare, she said, “Well, see, I think of time as a continuum. So I think I met with them from the beginning to the end.” She also said she couldn’t recall where she went to college or whether she had ever been arrested.)

In its new legal filing, Nederlander of San Francisco asked the court to revisit the dispute, arguing that allowing the Curran to present “Dear Evan Hansen” and “Cursed Child” would cause the Nederlander theaters “irreparable harm” in breach of an agreement between the families restricting competition. “Both ‘Dear Evan Hansen’ and ‘Harry Potter’ are multiple-Tony-Award-winning, smash-hit Broadway shows that will draw huge crowds of theatergoers to the Curran,” the complaint says. “There is only one opportunity for a theater owner or operator to be the first to stage these sought-after productions in San Francisco.”

The Nederlander filing said that productions of the shows at the Curran could endanger subscriptions to the Nederlander company’s business, saying “a subscription is only attractive to theatergoers, and thereby successful, if SHN can offer the must-see productions in that area. Otherwise, theatergoers will abandon their subscriptions.”