FAFSA is a financial aid application form , not an aid distribution spot. The FAFSA does not give aid. The federal government and the schools give the aid.
With regard to federally funded aid…yes, you can submit the FAFSA after school deadlines to get any portion of the Pell Grant you are eligible for…and to access the Direct Loan.
BUT in terms of institutional aid, if you submit after the deadlines, don’t expect the colleges to give you aid from their money.
Best plan…if you need aid submit in keeping with the deadlines for your colleges.