Generally every employment agency is a unique company which is attempting to get as much business fro themselves as possible. So they will not share employees. If you want to get as much work as possible you could always sign up with multiple employment agencies.
Yes in the state of Ohio most employment agencies work together if they are in any part paid for by the state or federal government. Local organizations or private ones may also work with some but are not required to in the way that the government organizations are required to.
