can I work with different agents in different area?

We just started looking for houses but haven't decided which area to buy. We have a agent who is specialized in the area we don't like and she is not really good in other areas. Can we work with another agent in other areas? and the agent whoever introduce us the house will get commission. Is this ok or illegal or ethnically not correct? We haven't signed contract with any agent yet. Thk you in advance for your reply.