I play 2 games w a partner. She continually adds an additional 2 games which she plays til it resigns...

If she plays multiple games with you at the same time, just play these games with her as well, you shouldn’t lose the game as long as you play your turn in each game. I play multiple games with the same person at the same time and have never lost due to resignation. If you don’t want to play with her just decline the game before you play a tile.