I think that would introduce a little too much down-time as everyone looked at their partner's cards each turn. Also, do they get to look at their opponent's cards before they decide to play the card? This would affect it a lot.
I think a simple variant could be this: "During your turn you may place one card from your hand on your partner's discard pile."
Really though, the main thing is that it really depends on what cards are on the table. Tables with 3 piling as a viable strategy would be more interesting. Duration cards would be interesting if they applied to your opponent. Attacks - not sure if they should apply to your partner or not. Probably not I guess as otherwise it'd make people avoid them too much, but it could be interesting if you knowingly go for the counter strat the matches up.
Another idea, your partner's discard pile is yours, in so much as you always discard there (no option), but when you shuffle up you shuffle up from the other one. It allows for a sort of 8-shaped 2-phase cycling of the cards, and could lead to some interesting imbalances in the deck-sizes if someone has a lot of draw and the other doesn't. However, I think this would unfortunately gimp the more extreme strats - drawing your whole deck would only work for one turn, as they'd all end up back in the other player's pile, and next turn you'd only have a few cards to play with, which literally be the hand they just played with. I suppose you could also end up with no cards to draw for next turn too. Hmmm. Balls.