The proliferating breach-of-contract suits, many of them filed over the last week, target some of the biggest names in higher education: state systems including the University of California and Arizona State, as well as private institutions such as Columbia, Cornell and New York University.

The students’ lawyers, advertising on sites such as Collegerefund2020.com, are seeking class-action status on behalf of hundreds of thousands of students. While legal experts say the suits face high hurdles, they could potentially involve billions of dollars in claims.

To justify annual prices that can top $70,000 a year, colleges have long advertised their on-campus experience, including close contact with professors and peers who will become a lifelong network.

Now, millions of students are instead studying online. Many of the suits are seeking compensation for the difference in value between the virtual and in-person experience. Plaintiffs include Grainger Rickenbaker, a freshman majoring in real estate management and development at Philadelphia’s Drexel University, which charges more than $50,000 in tuition and another $16,000 in room, board and other fees.