Playing Pokemon TCG with more than two players
The closest that I have found that meets your criteria and also only uses three decks (thus excluding "Two-Headed Giant") is a 3-player variant from BoardGameGeek, which was an improvement to a suggestion another gamer had made.


The three players are arranged in a circle.
A player can attack the player to their right for full damage.
A player can attack the player to their left for half damage, rounded up to the nearest 10.
Special effects (e.g. not being able to use item cards due to Dragonite's "Deafen" attack) can only be applied to the player to the right. (It seems that you are allowed to deal damage to the left player and have an effect apply to the right player).
The game is otherwise played as normal, and the first player to get all their prizes wins.


The advantage of this variant is that while teaming up is still possible, it's sub-optimal since one player will be doing less damage if they gang up, so it's only likely to happen at critical moments.