Is the aid award from your first-choice school insufficient? The New York Times offers some tips for appealing here. A couple of key points in the article:

• Find out your school’s process for appeal and follow it. There may be a specific form, for example, or a person who handles all the appeals.
• Try to meet with someone in person to discuss your situation.
• Document your situation. Whether your family’s financial situation has changed or you’ve received better offers from comparable schools, make sure you can prove it.
• Don’t delay your appeal. Particularly with need-based aid, there is a fixed pool of money available. Waiting to appeal may mean it’s no longer available.
• Keep your expectations reasonable. Mark Kantrowitz of Edvisors estimates that only about 1% of appeals result in an adjustment.

Good luck!