Four way chess -checkmate My friends and I have been playing knightmare chess in a four player variant. We were playing with the stipulation that when a player is checkmated, after his turn he removes his king from the board and his pieces change allegiance to the last player to cause checkmate.
I had caused checkmate on a player. An opponent between my turn and the checkmated player moved his bishop to cause check on the same king I had checkmated. He staked a claim to this player's pieces. I refuted his claim on the basis his bishop did not cause checkmate, only check while my pieces actually did cause checkmate. Who would get the pieces?
By definition, check is a move where a peice is threatening on his opponents next turn. According to this, I argued that I caused checkmate and was entitled to his peices.
I will need to make an educated guess as to what rules come closest to what you have described, and I think it is that:


You are checkmated whenever your king is attacked and if it were your turn next, you would not have any moves that would result in your king not being attacked.
An opponent causes checkmate on you, if at the start of their turn you are not checkmated, but at the end of their turn you are.
If at the start of your own turn you are checkmated, then your king is removed from the game and the opponent who last caused checkmate on you will gain control of your pieces.


Under these rules, merely piling on a check while it was already checkmate would not cause checkmate.

The rest of this post is background and further analysis of checkmate, that informed my answer and may help to understand it:

According to Wikipedia, it was the Persians who abandoned king capture and introduced warning of check in order to not accidentally end the game.  So let's go back in time before the introduction of checkmate and reanalyse.

In two-player chess checkmate is a situation where at the end of your turn all parties are certain that you will (be able to) capture the king on your very next turn (and in two-player chess there exist no reasons not to actually capture the king).  Because of this certainty of how the next two turns will play out (a doomed evasive move and a certain king capture), there is no point in actually playing those moves, so both can be (and have been in FIDE chess) eliminated from the game with no detriment to the game.  (Very much the same thing happens when a player forfeits the game upon realizing that the game is lost and there is no point playing any further.)

But if there are three or more players a third party can intervene on behalf of a threatened king and (unless the game ends when the first king is captured) there may be more pressing matters than capturing an opponent's king left in check (like defending your own king).  These differences make it impossible to say with certainty when king capture is actually going to take place before it actually happens, thereby invalidating the reasoning which allowed us to eliminate king capture from the (end of the) game.

It is of course possible to try and use a definition of checkmate that is equivalent to the full checkmate described above in two-player chess also in chess with three or more players.  Indeed checkmate is usually defined in an operational way that is equivalent to full checkmate in two-player chess: your king is attacked and you have no move that will result in your king not being attacked. 

When you try to use that definition in multi-player chess you will need to think about on which player's turns one can be checkmated.  If your king is attacked and you have no move that will result in your king not being attacked, because it is not even your turn, are you checkmated?  Apparently that was something you rejected, but then it becomes hard to say who checkmated you.  It is possible for example that the player before you causes your king to be attacked by moving one of their pieces out of the way of a third player's piece, and even causes you to not have any moves that result in your king not being attacked, even though they are not even checking you with any of their own pieces.  Have they checkmated you?  I think most people are inclined to say yes.  But if you want to know if they caused checkmate or not, then you need to be able to say whether or not you were already checkmated before their turn or not.  Thus you need a way to determine checkmate even when it is not your turn.

One extreme is to say that every check from a player not immediately before you is checkmate (because as it is not even your turn you have no moves to remove that attack).  Another way is to pretend that it were your turn and see if you could do something.  I have recently even read rules for multi-player chess where it actually becomes your turn if you are checked, and the player whose turn it would have been had you not been checked continues after you (and you may or may not forfeit you actual next turn).