You do, but they supplement each other so you don’t get any additional money since they are both under the same category of need based financial aid.
In a (very) oversimplified example:
Say B&G is set to “give” you $13k toward tuition. If you receive an additional Pell grant that gives you 6k, then they would reduce your B&G allocation by the equivalent amount of 6k so that 7k comes from B&G and your total aid still remains 13k. The only way to get gain additional financial aid is through merit based aid to overcome and not need based aid.