Contact your school's financial aid office. The first step is opening up the lines of communication. Your school may have a formal process for a financial aid reevaluation, which you should know about.
Explain circumstances that may not have been included in the original application. For instance, most applications rely on the previous year's financial statements. If your family has suffered an income loss, this wasn't considered when the school determined your financial aid package. Letting the school know about such circumstances can prompt a financial aid review.
Show the financial aid office the packages that other schools offered. In some cases, a school can be swayed to offer you a financial aid package that is more in-line with what other schools offered. Some schools will not take this into consideration.
Ask the adviser for help. The financial aid counselor does want to help you attend college. If the college is unable to offer you more financial aid, the adviser may at least be able to explain your options. While grants are preferable because you don't have to repay the money, you may be eligible for additional low interest loans, which you can use to pay for college.