Not sure if this behaviour is intended.
I can log users without problems on multiple devices with your Game Center SDK add-on.
But if I connect a different Game Centre user and then try to connect to my game, i receive an ACCOUNT_ALREADY_LINKED error from the server.
From the server side It seems that the client try to log using account of the previous Game Center account with the wrong credentials.
Is this happening when trying to authenticate another user on the same device as the previous user ? The "ACCOUNT_ALREADY_LINKED" error means the current player has a GameCenter account liked to them but it doesn't match the one they just tried to log in with. Are you getting a fresh token for the second user when they Authenticate. Is it a GameCenter authentication directly or are the users authenticate by device or userName/password before the GameCenterConnectRequest ? If you have any logs please attach them to the thread, or if you can let me know the gameId I'll take a closer look at the game for you.