Credit Transfer After Getting Associate's

Do most colleges only accept 60 credits when transferring after graduating with an Associate’s degree? When I graduate, I’ll have at least 70 credits (I had about 30 dual credits from high school when I began attending my community college last summer.) I will most likely be looking to transfer somewhere in Illinois (possibly Indiana or Missouri.) What most likely would happen to my credits with an Associate’s degree? (I was told that with the degree the credits would transfer.)