It depends on the school, but I would say approach it with confidence! You are a candidate that they want and you should assert yourself respectfully. Say you really want to matriculate, and that finances aren't the only factor in a decision, but increasing your award would really enable you to attend that specific institution, your top choice. Offer any documentation of other offers if you have them. If not, address how alleviating your financial burden might make it possible for you/help you excel in the program.
I hope this helps.