Can we both claim him?

Okay, I've never been eligible for financial aide because my parents make too much. I just had a baby though, so now I will be considered independent & should qualify for Pell. My SO & I live together, but are not married. We are both going to be filing a FAFSA. I know for tax purposes only 1 of us could claim the baby. Are we both allowed to claim him on the FAFSA?