According to other comments here, and some of my own ideas, we can write about other kind of subvariants.
It is not mentioned what happen in case of attacking partner's pieces. Here is some possibilities of subvariants to deal with it
Attacking partner's pieces is not possible.
It is allowed to capture partner's pieces (other than a king), but you are not in check if being threatened only by a partner's pieces.
It is allowed to capture partner's pieces (including a king), and there is no check/mate (and therefore you can castle into/out of/through check); you need to capture the king.
One kind of subvariants can be the teams:
Partners across from each other.
Partners next to each other.
No teams.
Washizu-style: Partners next to each other, with one player of each team designated as "leader" and one as "supporter". The "supporter" plays immediately after the "leader". Your team instantly wins if the opposing leader's king is captured (or checkmated, depending on subvariant).
And there is winning conditions:
Russian: If you are checkmated, all of your pieces (including a king) is removed from the board and you take no more turns. Any team out of players loses.
West-European: You pass if you have no legal moves (for kick-the-king variant, also if you have no king). Checkmating both opponents simultaneously wins.
My rule: If you have no legal moves or if your king is captured, you pass your turn. If both players of a team pass without either making a move in between, that team loses the game.
Bradley's rule: Whenever a player is checkmated (or loses his king in kick-the-king), all of that player's pieces are changed to the color of whoever checkmated/captured him.
Lastly, there are subvariants dealing with fortress:
Normal: Each player deploys his three additional pieces inside the fortress at his own choice and it is then visible to everyone.
Hidden version: Variant of the above where you cannot see opponent's pieces in opponent's fortresses (you can see them in your/your partner's fortresses, or when they are in the main board, and you can still see your and your team's pieces in any fortress).
Random hidden version: Further variant where in addition to hiding pieces like that, the pieces are deployed at random in valid positions (individually for each player).
According to other comments here, and some of my own ideas, we can write about other kind of subvariants.
It is not mentioned what happen in case of attacking partner's pieces. Here is some possibilities of subvariants to deal with it
One kind of subvariants can be the teams:
And there is winning conditions:
Lastly, there are subvariants dealing with fortress: