Several years ago, she created a tool that helped families more easily compare estimated prices using colleges’ individual net price calculators. Many selective institutions blocked her tool entirely, as if making this all easier was some kind of sin. The comparison tool is no longer available.

Presumably financial aid directors, whom Ms. Seldin consulted before starting SwiftStudent, won’t disparage her efforts this time, given that the tool is designed to make their lives easier.

Your chosen school might have advice, too. During any appeal, Job 1 is heading to the school’s financial aid website and seeing if it has useful guidance, such as a particular form for reconsideration requests. The University of Denver, for instance, has an excellent page explaining what sort of changes in financial circumstance are grounds for appeal when asking for more need-based aid.

Your school may also offer money in another form: merit-based financial aid. It’s generally based on academic performance, leadership or other skills. And Todd Rinehart, the University of Denver’s vice chancellor for enrollment, said in an interview that there was nothing greedy about asking for more of that, too, even if you aren’t in the middle of an unfolding crisis.

How can that be? Let’s say you want to lower your annual cost from $50,000 to $45,000 by asking for $5,000 more merit aid. If the school figures that its cost to educate each student is, say, $38,000, your $45,000 can still help the students who can afford to pay only $25,000. If that’s the case, the college may still want you to come and stay until graduation.

Schools like Denver also understand that there may be similar colleges offering you more merit aid. If that’s the case, it certainly can’t hurt to send a polite, measured request pointing out your other, better offers. Also include any proof that your academic performance or standardized test scores have improved; a school may have a formula to help administrators determine merit awards, and you may have vaulted to the next level in the months since you applied for admission.

If this sounds like too much, more hands-on assistance is available.

A start-up called Edmit — founded by Nick Ducoff and Sabrina Manville, two former college administrators — has a free college-shopping and pricing tool. For a $99 annual fee (though some families pay nothing through partnerships with schools) plus $30 for every 30 minutes, you can get access to its network of advisers, who will hop on the phone and coach you through any appeals you want to make.