Consider the stable marriage problem, where both sides want to match with multiple individuals from the other side (perhaps a fixed number, or perhaps within some range). Something like, if doctors could choose to go to more than one medical school at the same time.
Is there a variation on the deferred acceptance algorithm to handle this generalization? Can I just have each "doctor" propose to n hospitals at each step, where n is the number of hospitals he is trying to attend at once? Also, what if hospitals do not have preferences?