Can you mulligan in the middle of a game of Magic the Gathering?

I was judging for a beginner tournament of MTG, and although the kids were all supposed to be new players and playing creature only decks we had a few kids who showed up who had been playing quite a while. I had stated at the beginning that only the paris mulligan would be allowed, but one kid wanted to mulligan in the middle of the game. After reading the wiki, I wasn't sure if it was supposed to be allowed or not, but I ruled in favor since both players were okay with it. Did I make the right call?