Many schools are willing to reconsider their first offer, especially for a student they really want.
Most say they reconsider only if presented with new information, so you will definitely want to contact the aid office if you can come up with ways your financial situation has changed since filling out the forms. Your father may have been laid off, or perhaps your grandmother has taken ill and your parents are contributing to her care. If a family can go back and be very specific with numbers, nine times out of 10 they will be successful. A more direct approach is to ask one school to meet or beat the offer of another. Carnegie Mellon invites students to notify the school if they have received better packages from other schools.