I watch wrote:
I am unaware of any distance runners who tried to get their offer increased by providing an offer from one Ivy to another.
I expect this is rare, but I know for a fact (direct from coaches involved) that this does happen and that the coaches make the possibility very clear when they're recruiting the athlete.
I agree that Ivy coaches usually reserve their "pushes" for kids who apply ED, and thus get their recruiting for next year finished or nearly finished in the fall (must be nice!), but there certainly have been at least a few examples of athletes' playing one Ivy against another.