“Yale often claims that the university cannot punish the fraternities because they are unregistered, off-campus organizations,” the lawsuit says. But it argues that this position is disingenuous, because the fraternities “act as extensions of Yale,” providing party space, while Yale permits them to use the Yale name, Yale email addresses, Yale bulletin boards and campus facilities for recruitment.

Peter McDonough, general counsel of the American Council on Education, a university trade group, said universities have been reluctant to become too deeply involved in regulating fraternity life.

“The very concept of a campus is where people learn not only from each other but through shared experiences,” he said. “And this isn’t the K through 12 environment.”

The plaintiffs — a sophomore and two juniors — have demanded in the lawsuit that Yale and its fraternities rein in the parties. They have also asked for a court order that would force the fraternities to admit women and allow them to share in the benefits of membership, like housing and powerful alumni networks that can lead to jobs, internships and social capital.

“Simply put, fraternities elevate men to social gatekeepers and relegate women and non-binary students to sexual objects,” the lawsuit said. “Moreover, Yale’s fraternities have alumni and professional connections to the business world, including banking and consulting firms, which often result in coveted job offers and economic opportunities.”

The three women who filed the suit are Anna McNeil, 20, a junior from Brooklyn majoring in art history; Eliana Singer, 19, a sophomore from Minneapolis majoring in political science; and Ry Walker, 20, a junior from Brooklyn majoring in astrophysics and African-American studies. The law firm representing them, Sanford Heisler Sharp, is also representing women who are suing Dartmouth College for sexual assault and discrimination by three professors who they said turned a human behavior research department “into a 21st-century Animal House.”

All three women in the Yale case said they were groped at fraternity parties during their first semesters. In the lawsuit, Ms. Walker, who is African-American, said she was passed over by fraternity brothers controlling admission to a party, while white women behind her were admitted.