RP1 comes into the game, as a non-starter.
RP2 comes into the game and RP1 goes to 1B.
RP2 blows up. Can RP1 come back to the mound?
This occurred in our game, where the opposing coach protested after RP1 had thrown 1 pitch after coming back to the mound. The umpire had us pull RP1 (after that one pitch) and replace him on the mound with an "eligible pitcher."
Again, RP1 was not an original starting player, but did not leave the game when RP2 entered.