Sounds like there are only two legal ways to do it in this case: Flight instruction or safety pilot.

You cannot do unlimited flight instruction, it has to be for valid flight training purposes. Since you are new to the airplane that qualifies as a valid reason for flight instruction. You could reasonably do that for many flights in an airplane as complex as a king air. But you cannot do it forever...if you log dual received for hundreds of flights, that will not go over well with employers or the FAA (they will revoke your tickets).

If the guy wants to let you fly under the hood, I think you can do that as much as you like...nobody ever has too much IFR proficiency. That would look better for employers too...many airlines do not count dual received the same as actual PIC.