You can have either three other Pokémon with you in dungeons, but your allotted size limit cannot surpass six stars.
For example, Articuno is size four. If you want him in your team, you can either have one size two Pokémon, or two size one Pokémon.
And while in Pokémon Square and whatnot, it's just you and your partner until you beat the game. Then it's just you.