The student loans in your financial aid offer represent the maximum amount of government loans that you are eligible for. Either you're getting the absolute annual maximum, or you're getting some lesser amount that is determined by your financial aid need. Either way, you can't get more of those.
If you need additional money to survive while you're in school, your options are fairly limited:
1. Your parents can borrow from the PLUS (Parents' Loan for Undergraduate Students) program
2. You can apply for a private student loan
3. You can work part-time while attending school.
If your parents are willing to help, option 1 might be the best alternative. Like the Stafford loans that you already have, the PLUS program is a government-backed school loan program, with low interest rates, and reasonable repayment terms. However, unlike the Stafford, the PLUS loan is a credit-qualification loan, so your parents will have to satisfy the lender's credit analysis.
Alternative 1-A is getting a part-time job. That's easier in some places than it is in others. If you're going to school in
a little college town that is miles from anything else, finding a job could be a tall order. On the other hand, this is far and away the most responsible choice - this is what people do when they need money to afford things - they work.
The private loan option is easily the least desirable, but it will be the most difficult, too. As recently as two or three years ago, private student loans were much more readily available, and many students borrowed (in most cases far too liberally) to make it possible to afford school. Those days are over, at least for now, because the worldwide banking and lending crisis pretty much destroyed the private student loan market. If you apply with one of the few lenders that are making these loans (Chase, Discover, Wells Fargo, Sallie Mae, etc), it's about 99.8% likely that you'll need to provide a very highly creditworthy cosigner.
Best of luck to you - talk to your parents about the PLUS and get out there and look for a part-time job that you can juggle around your school work.