Q; Can I accept extra work/pay from another college within the s

I have a full time instructor position in a university and hold a H1B visa.
I currently have a opportunity to work on a project for another college of
the same university and get paied. Can I do that with my H1B visa? What do i
need to do when filing the tax forms? I do have a EAD card that has never
been used and I do not want to use it since it will nullify my H1B.

Thank you in advance!