The current World Mind Sports event in China has a number of different styles of chess, including the relatively new format of Basque Chess. In this format players play two games at once, against the same opponent, starting one game with black and the other with white. Players move on either board (when it is their turn), in a similar way to a clock simul. The idea is to cancel out the advantage of having the white pieces in the first game of a 2 game (or 4 or more) match.
While this format seems to be new, my knowledge of a similar type of game goes back at least 20 years. FM Craig Laird described to me a 4 (and possibly a 6) board variation of the game, which he said was played at his local club. To make it more fun it was played with a blitz time limit (G/5m) for all games. It was even tried at the Belconnen Chess Club 25 years ago, although the format tended to favour fitter (and taller) players! Adding the extra games did add an extra strategic dimension to the match, as you could afford to abandon a losing position to concentrate on your winning ones. It would not surprise me if it still is a thing in certain chess clubs, although the necessity of having extra equipment may have contributed to its lack of popularity.