Phase Chess -- Variations
As mentioned in the intro, there are obvious variations about what to do with piece captures. The prefered: If it dies on board A, it dies on board B. The sticky: If it dies on board A, it can no longer move on board B. The subtle: If it dies on board A, it can make any move that is legal on all of the boards it's still on.
After one king is dead, the convention is that board is done. The others may continue on. But, there are other possibilities... the remaining pieces live on, the partner of the deposed King is now King of that land, or the board is still active (and thus still restricts opponent movements) but the Kingless folk do not move.
The normal game spends a great deal of time with partners discussing strategies that pack the biggest punch. I'd like to play sometime without partner communication. It could cause some causality problems. I would recommend then that the partners moves not be considered "simultaneous" here, but that they be a "first-come, first-server" scenario. Thus, if one partner makes a move that is "legal at the moment" then the other partner must make da move from what is legal at the "new" moment.
This variation requires players with sharp eyes for the game. This is similar to silent partners except that you only get to see the boards you're playing upon. Again, "simultaneous" partner moves may be tough to enforce in this variation.
We made an exception to the capturing rules for pawns to be able to get them out of the way. One obvious variant is to ditch the exception so that a pawn can't attack on one board unless it can attack on both. I think this makes for an extremely crowded game.
Of course, finding four folks who are into playing is an order of magnitude more difficult than finding two folks who are into playing. So, go ahead, play both of your team's corners.
Why stop with just the four-player, two boards per person scenario? Any polygon with an even number of sides is a good place to start. Six-people with two boards each, or six-people with three boards each. Any bipartite graph should do nicely. But, people with higher valences are probably at a great disadvantage.