In Illinois, 2 bucks total regardless of weapons or seasons hunted. As many does as you want with bow per paid permit.

For me 3 is the most I will take unless a landowner wants an extra doe harvested and the population/buck to doe ratio warrants it. I try to take one mature doe early for the freezer to be sure I get some meat, and then big buck hunt. Of course in that case one doe is all I might get!