you don't know 3-check in regular chess? same thing.
[4PC Variant]: N-Check

Also, what would happen if you mix N-Check with Capture the King? Especially when someone has 1 life left.

It is possible to mix N-Check with Capture the King. You can check your ideas on the Analysis Board.
New Game -> Analisys Board -> Edit position (bottom right corner) -> enable Capture The King and select a number in N+.
Each player's king starts with N lives and will lose a life each time he gets checked. (Getting doublechecked will cost 2 lives). The the final check will be checkmate.
In N-Check, kings will have a number indicating how many lives they have left.
In teams games, a player with 0 lives left will only get checkmated on his turn.