There are housing exchanges, but the key word is "exchange." My understanding is that you have to find a student at another campus who will swap with you, and then the two of you 'draw' (hall draw...the lotto process of choosing rooms) for one another.
They definitely do happen, but they're not common. I knew a girl who went to live on Mudd because she liked the dorm communities; a girl lived on Pomona because her major was on Pomona, as were many of her friends. Each of these was for one year...I don't know if there are rules re: how long you can do a housing exchange. One friend talked about living on Pitzer because her close friends were there, but I don't believe she ever actually went through with it. I generally had a few (1-2) off-campus women in my Scripps dorms, too.
Sorry...I'm not familiar with the details of the process. Good luck finding more info