Can I exceed my total Federal Work-Study award?

According to my FWS award for American University, I could only earn 900$ per semester which is certainly not enough. Is there a possibility I could work to earn more?

No. See https://studentaid.ed.gov/sa/types/work-study#can-i-work-as

You can’t earn more using work study finds. BUT some college jobs are funded with work study funds and college funds. My daughter worked at a job that was work study. When her work study funds were used up, she was paid out of university money. But this is not the case with all jobs…so you have to check.

There are also jobs on most campuses that are funded with money that is not work study money.

Right, you are not prevented from working a non work study job for extra hours. Either in the same position, or another university position or a non university position. Try not to work more than 15 hours a week, 12 is better so you can have time to study.