I’m not up to date on current transfer trends at all, but in the past (including the not-so-distant past) a lot of transfers into elite colleges were people coming from other elite colleges. Not all transfers, by any means, but that was definitely one of the themes. In many cases, the transferring student had had been accepted by the new institution out of high school, but had decided to go elsewhere. There used to be any number of transfers among Harvard, Yale, and Stanford. (I think it’s only very recently that Princeton started admitting any transfers at all.)
I don’t think it’s remotely true anymore, but in the past I believe there was essentially an open door for students who had been accepted at Harvard, but chose to go to Deep Springs, to finish their bachelors degrees at Harvard after their two years at Deep Springs. There used to be 2-3 such students per year. (It’s telling now that Harvard does not appear on the list of where Deep Springs AAs “most commonly” complete their undergraduate education. There’s a Crimson article from '00 online that talks about the eight Deep Springs alumni who were then juniors or seniors at Harvard College.)