Around now, university officials might usually take a deep breath. Campuses are emptying out for the end of the academic year. Gone, for the most part, are the tent cities that student activists erected as a symbol of opposition to Israel’s war in Gaza.

But this summer might feel longer than most.

Congressional Republicans have promised to press their investigation into college antisemitism, even as they have completed their latest hearing, which they tried to turn into a public shaming session for the leaders of Rutgers, Northwestern and the University of California, Los Angeles, over their handling of campus encampments.

And protesters have likewise promised not to give up — with hundreds walking out at Harvard’s graduation on Thursday, and students at U.C.L.A. pitching new tents and briefly taking over a building.

Over the next few months, colleges will need to navigate a complex set of challenges. There are ongoing federal investigations at scores of universities and school districts over their handling of antisemitism claims. There are hundreds of discipline cases to be decided. And plans are needed for the fall, when college quads will fill back up just a couple of months before the presidential election — possibly with more protesters.

Here is what may keep university presidents up at night.

One of the major takeaways from the hearing on Thursday was that the three universities had yet to resolve scores of disciplinary cases involving student protesters.

The chancellor of U.C.L.A., Gene Block, said on Thursday that the school was conducting more than 100 investigations into student conduct involving both antisemitism and Islamophobia.