Chances are you would need to file for Foreign Qualification in each of the states where you will have big clients. Depending on the type of service you provide and the state you might have to also register for a state tax ID and obtain specific licenses.
Sometimes if a company has clients in another state it might not need to register in that state, and other times it does. It mostly depends on the state and the level of involvement. In your case I believe it would be safer just to have those registrations completed.