Based on Bughouse Chess.

A unit your partner captures on one board becomes your unit on another.

Bughouse is certainly possible with multiple instance of the same game (e.g. Acquire). Hard to do with money because it's immediately useful to you, but you could ignore this and pass it to your partner. FungiBills can also harmonize Monopoly and Acquire money (say), to be passed from game to game.

Pseudo-Bughouse? Roll a 6-3 on dice in one game, draw a 6-3 domino in the other?

How to do Bughouse with more than 2 games or 2 players/game? Circular Bughouse?

Chad Urso McDaniel? points out that one of the "FF" games has multiple boards your piece can travel among.