This is a hard thing to do properly and easily (TriNet I believe does it well, but they are not as inexpensive as Gusto). And many state still are behind the times and you can't file on the website and have to mail in compliance reports or pay for access to a special system etc. Kinda stupid if you ask me, but I've dealt with it too.
What you could do is have him declare a home state (primary residence), maybe his parents state or something, and as long as he isn't spending long periods in another state he would be considered a traveler and not subject to local state employment taxes generally. Of course, if he gets a new drivers license etc then that won't work. This is how you handle traveling consultants who might literally spend the next 6-9 months in one state for a job, but they are permanent residents of their "home" state for tax purposes etc. He can even have mail temporarily forwarded to the state he is in, just not permanently forwarded.
You should probably talk to an attorney or tax accountant just to get the details right, but I did this for years with my consulting teams and we were always on the right side of the law. Only place that it gets more tricky is the north east area with their shared burden on taxes etc. But if he can avoid his home state being one of those then you are probably pretty safe.