Spawning multiple characters per player

I have a game in which the player is meant to have three characters and switch between them using pawn possession. This works fine in singleplayer, but how would I get the multiple character logic to work in multiplayer? Currently I have three instances of my TopDownCharacter, which is clearly impractical. The trouble is, when a network player connects, only one character is spawned at a NetworkPlayerStart. How do I spawn three characters and hand control of them to the controller?