Structure of multiplayer card game?

Options
I've programmed a word rummy game for one player against three robot opponents. What components will I need to adapt it for multiple players?

I can call it using the PunBasics-Tutorial demo project, but that only creates multiple versions of the game which don't interact with each other.
(I can see that it works very slightly, even though that project wasn't designed for games like mine. When I combine both, I can see a player's name and status bar - but not the robot object - making slight movements among my cards.)

My game actually doesn't feature any movement except for dragging and dropping cards. The tabletop area contains a face-down deck of cards, four discard piles, and cards previously melded. Active players can drag a card to their hands, and play words (card combinations) to the table, including adding to an opponent's word. Inactive players have the same view, but can't interact with anything on the table.
Each player has a hand of cards which the opponents can't see. I don't know if this would be part of the tabletop, or a separate panel.

You can see the game at http://deanhoward.us/Anim-Abet-intro.htm
If I can re-learn how to use it, I'll put the project somewhere under github.com/nightrider518

This wheel has probably been invented many times, but I haven't found any code or tutorial to use as a starting point. Can someone point me in the right direction?

Thanks,
Dean