An actor can have only one owner (or none at all (default)). This is necessary to determine which client should receive Client RPCs, and also whether a given client can send its RPCs to the server.
Becoming an owner is very simple - call the SetOwner function ON THE SERVER and specify the client player controller (or character, or another actor that the client already owns) as the new owner.
To simulate multiple ownership I use a method I call RPC Tunnel - for each client I create an actor that it owns, and through this actor I call events in the common actor. I think you should do the same.