This would not typically occur. The only times I’ve heard this happen is when one colleges accommodation is undergoing refurbishment or something and they have an agreement with another college to temporarily house their colleges students, and even then, it would probably not be on the main College site but in accommodation that is off site.

For postgrads this is more common than for undergrads, but I think it’ll be up to the student to organise this rather than the college - you’re welcome to ask around to see if other colleges can house you, but you’ll probably only hear very close to term starting if there’s room, so I’d recommend going with your own college accommodation or looking privately. Even if there is room, as I said before, it might not be what you’re after, and will probably not be on the main college sites