There's a limit to what you can borrow from the government, and if you need more than that, then you make it up with private loans (often higher interest).
However, you can only borrow up to what the school determines as the budget needed. Sometimes they increase the budget for child care, but that's about it. Budgets are designed for the student only, and consideration isn't usually given for family. However, there are some places that you can get a student loan through that doesn't certify with the school. For example, I borrowed from Suntrust to pay off some debt that I wouldn't be able to make regular payments on with the budget I have. Interest rates are even higher for these loans, and you have to make sure it's a loan that does NOT certify with the school, because they'll reject you because you're already at the budget max.
It sucks that they put limits on it. (Not the federal aid, but the overall budget). When we're going into this much debt, I think we should have the ability to decide if we want an extra $5000, and not at a really high interest rate.