Employment Law Questions? Ask an Employment Lawyer.
Did you sign a release of claims, which is generally required when receiving such severance?
Unfortunately that is the case - you couldn't make a claim because you would have released the university from liability for any and all claims that would have arisen out of your employment in exchange for the severance payment. There would be no other option in regard to getting recourse from the university. You could ask the university again for more severance, but there would be little to no incentive for them to do so because the release; i.e., they have nothing to gain by giving you more.