Leveraging multiple M7 offers for scholarships

Using throwaway account b/c my main account has too much info that could identify me, and its impossible to ask this question without coming off as super entitled.

Am fortunate enough to be in to Chicago Booth, Berkeley Haas and Columbia, and still waiting to hear from Kellogg. No scholarships at any, although it sounds like Berkeley and Columbia wait until early next year to offer certain scholarships.

Does anyone have any experience negotiating with schools in order to get $ once you have multiple offers? If so, what is the best way to approach? I have a lot of thinking to do in terms of where I go, but significant tuition aid could definitely tilt the decision in favor of a given school.