An optometrist I shadowed did this, transferring from Berkeley to SCCO after her second year due to a family illness. This was a while ago (at least 15 years ago) and she said it happens very rarely and only with a good reason. She made it seem like "not liking" the school you're at probably isn't reason enough.
One of my classmates transferred from PUCO to UCBSO after his first year. This was in 1993. I know the dean of PUCO at the time (Les Walls, I think) was not happy and made it sound like it would be difficult, but my classmate said it was really not that hard. He was a sharp student, and won the top honor at our alumni awards dinner, so I am sure that made it easier for him to do it.