It's not entirely a shared-deck format, but I have been theorizing something kind of comparable. Haven't made an actual card list and playtested it yet though, but the broad strokes are:
- Small decks, 10 cards, maybe a few more, with no lands
- Lower life total, let's say 10 for consistency
- Drawing from an empty deck makes you lose 1 life
- Starting hand size is lower, in the ballpark of 5
- The player going second gets a free
Wastes into their hand
Make a deck either by just grabbing some random cards from the cube, or use a quick draft-method to get enough cards, you won't use them for more than one round. The game starts with a collection of basic lands, and maybe some curated set of nonbasics, in exile. The gimmick is that, once on your turn at sorcery speed, as a special action, you can swap a card in your hand, with any card in exile. You are basically exchanging them, but from a rules POV, it's more accurate to say that the two cards perpetually become copies of each other, but even that is probably not entirely accurate. Any references to the exiled card persist on the new one, you don't lose any counters. In effect, it doesn't become a new object, they just magically took the place of each other in the game.
The level 0 gameplay of this is pretty basic. You have to swap cards in your hand with the lands so you can actually play spells. Later in the game, you can throw away the cards in your hand to pick up the cards your opponent tossed away earlier, and they can do likewise, so there is some tension between which cards you expose to your opponent and what color you want to move into.
When you take the card pool into account, it can get pretty crazy. If you
Swords to Plowshares a creature, you can choose to swap it with a card in your hand, in effect stealing it. You can keep rebuying the same flashback spell over and over by discarding a card.
Flickerwisp turns into a
Show and Tell, and Rebound also becomes a cheat mechanic, but importantly one that your opponent can easily disrupt. Playing around a
Banisher Priest or
Suspend can get really strange.