Once they approve you I think you are locked. As far as how much you can get, that depends on a few things, the biggest being the difference in the in your school's cost of attendance and the amount of other aid received.
The Cost of Attendance is things like tuition and fees, but also non tangibles like books, room, board, living expenses, etc. So say your schools cost of attendence is $38K (which mine is) and you are approved for $18,500 from the feds (this is per two semesters, for me, spring and summer 06) the difference is in the $14K range. After the stafford loans pay my tution, I still owe about $3000 out of pocket for tuition and fees and the rest goes to me directly, in theory to pay for room, board, books and other such living expenses.
Most private loans do it this way, but whethere or not you get approved for the full amount you request, I don't know. I personally did and I had a crap credit score and had been denied across the board until I applied with sallie mae law loans and they gave me the whole shebang and it was really easy.