I know a couple of kids who have done it. In the case with which I’m most familiar the kid in question was admitted to a c. 60% SSAT and a 90% SSAT school and originally chose the 60% school for reasons of fit. After a year they felt they weren’t being sufficient challenged and reapplied to the 90% school and were admitted. They did well enough at the school that they ended up at an Ivy League college. No sports or repeat involved. Also no mega-donations.
The other case I’m less familiar with but I believe it had to do with a mismatch in school culture and was a switch from an 80%ish SSAT school to a 90%ish. Kid was a varsity athlete but not a recruitable one, just a run of the mill contributor. Nice kid, stellar grades. Not a repeat.
I’ve seen lots of kids move the other way when they had difficulty at the tougher school.