The most likely scenario for a reshuffle is probably in the Eight Game Mix where 2-7 Triple Draw is played 8 handed. So 40 cards will already have been dealt, 1 burned, leaving only 11 cards for the first draw. Then the folded hands (if any), and then the discards.
This is quite a strain for the dealer, constantly trying to keep track of how many cards you have available for drawing.
I'll be playing an Eight Game Mix in a few months if I can get enough players

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Let's say it's 8 handed, and 2 players fold before the first draw.
That leaves 11 cards in the stub after burning, and 10 cards in the muck.
First draw:
The remaining 6 players draw a total of 17 cards. The discards are set to the side, The stub is dealt completely, leaving only the cutcard. The muck is then reshuffled, cut, and another 6 cards are dealt, leaving a stub of 4 cards.
In the following round of betting 1 more player folds.
4 cards left in the stub, and a muck pile of 22 cards (17 discards + 5 folded cards).
I'm thinking here that keeping the folded cards out of the muck to be dealt first doesn't accomplish much since at least some of the discards would have been discarded by the player who folded, and the folded hand could possibly hold cards that have been discarded by the other players.Second draw:
The remaining 5 players draw a total of 9 cards. The 9 discards are set aside.
1 card is burned, and the remaining 3 are dealt.
The muck is reshuffled, cut and the remaining 6 cards are dealt, leaving a stub of 18 cards, and a muck pile of 9.
In the third round of betting nobody folds.
Third draw:
The 5 players draw another 9 cards.
1 card is burned, 9 are dealt, leaving a stub of 8.
Final round of betting.
This seems like a reasonable way of doing it. That way you would only need to keep the folded hands and discards separate for the first draw (2 piles), and after that you'd only need to keep the discards separate from the muck (also 2 piles).