Proponents say unionization would help secure better health coverage for students and stronger protections against sexual harassment or discrimination by faculty members who exercise significant power over their professional futures. National labor organizations like the United Automobile Workers and the American Federation of Teachers have provided graduate-student unions with advice and training.

But while these unions have existed at public universities for decades, administrators at many private institutions contend that unionization would create a more adversarial relationship between teaching assistants and professors, undermining the university’s academic mission.

“Graduate students are students, first and foremost,” the University of Chicago’s provost, Daniel Diermeier , wrote in a message to the campus community in June. “They come to the university to study, to learn how to teach future generations of students and to make original contributions in their chosen fields of knowledge.”

Since the 2016 decision, in a case brought by Columbia students, a number of graduate student unions have made impressive gains. Before the decision, only one such union had a contract with a private university. Now five do, and 15 universities have held union votes since 2016, according to researchers at Hunter College.

After years of resistance, Harvard and Columbia agreed to bargain. And last fall, union organizers at Tufts negotiated a contract that included paid parental leave, as well as a significant increase in the graduate-student stipend.

“Student workers have come together to fight for our shared interests, to fight for protections that we need to feel safe in our workplace,” said Colleen Baublitz , a union organizer and graduate student at Columbia. “We are really powerful in offering much of the labor that universities now rely on to run.”