If you can ensure that students can't copy the work or use it outside of school it should be okay. We use Plex Server to show legally obtained film clips in classes over our local network at the school. We copy films and load them on the server. Anyone who accesses these films must have to have access to our network. That access is protected via usernames and passwords of enrolled students and current faculty and staff. I don't know if your IT department has this set up to control access to your network, but in our system I believe it is perfectly legal as long as the material copied to your Plex server was legally obtained.
Below are resources I used to determine if what we are doing is legal.
U.S. Copyright Office - Copyright Law: Chapter 1
These guidelines are from the University of Texas. https://copyright.lib.utexas.edu/ccmcguid.html
At the bottom it has a list of institutions that endorse the guidelines. One of the institutions listed is the U.S. Copyright Office.
