I think that one does not require a new visa when you get a new I-20 all the time. If you change your status from an undergraduate student to a graduate student in a different university or change from a Master's student to a Phd student in a different university, you do not apply for a new visa just because you have a new I-20 from the univ. that you are going to. I did my undergrad at Concord Univ and am doing my grad studies at Michigan State under the same visa although obviously I have different I-20's from different schools.
