First, the plaintiff can NEVER serve anything himself. In your state, there may be exceptions for small claims. However, you really should still use the sheriff or a process server. If they are unable to serve the person, then your state law may allow service by publication.

Is the person just a sole prop type of operation? Is there an LLC or corporation involved? If so, you can look up the registered agent on the SOS web site for your state. You serve the registered agent. They have to be available for service.