One of the most common questions I hear from parents at my financial aid seminars is,
“Is it true that it’s possible to negotiate a better financial aid offer with a college if another school has given you more money?”
My answer is always that “negotiate” is probably the wrong word. You’re not buying a car. But if two colleges, especially schools who compete for the same types of students, give you two very different offers, you can politely ask the school who offered less to review your case. Any change in your offer will usually have less to do with haggling than it does with a financial aid office exercising what they call "professional judgment."
Before you call a financial aid office to ask for a review, read this article on finaid.org. You’ll have a much better sense of how professional judgment works and, I think, a better chance of getting the aid package you need.