Hi all, I went through all this financial aid nonsense last year and completely agree with BrainBuff - there are partial scholarships, and there is extra money they have to bargain with. Further, some people who are offered full rides turn them down, and then they offer the scholarship to someone else.
My advice is to be persistent. Make sure they know that Penn is the place you want to be and that finances are the only thing holding you back. Show them all the merit money have have obtained from other institutions. I know some people don't want to beg, but I certainly did. I kept in touch with the financial aid officers through email before preview, and then after preview I probably probably talked to them on the phone 4 times. But it did pay off, they did increase my award. In the end it didn't match the aid I got from other schools, but it was enough so that I didn't feel as bad about the amount of debt I will ultimately be in.
Talking about finances can be super awkward, but you have to do it. It can only ultimately help you in the end!