Is there such a thing where one parent can have full physical custody and both can have joint legal custody?

My boyfriend wants to move out of the state to pursue his education and the mother wanted to seek full custody. My boyfriend has full physical and legal custody right now. The mother is okay with us keeping full physical custody of the child but she wants joint legal custody. Is there such a thing called that...? can we go to court and have it where we keep full physical custody but the legal is joint?Is there such a thing where one parent can have full physical custody and both can have joint legal custody?
No, but it is possible to have joint custody where the parents have the child equal parts of the time, but one parents residence is the primary residence considered for school attendance. What I am wondering is why all of a sudden does mom want joint legal custody. Also, does your boy friend have legal custody of the child or has mom just let him keep the child. If he already has custody legally and there is no provision that he can't leave the state with her, then he only has to figure out with mom about the visitation. I think he needs to contact an attorney.Is there such a thing where one parent can have full physical custody and both can have joint legal custody?
NO