It's possible to empty the supply in 2 turns with multiple opponents, I forget exactly how many are necessary. If we count each player's turn as a full turn the answer is three. With fractional round you can probably get it down to 1.5, possibly emptying the whole supply.
Okay, let's see. 6 players.
P1T1: Noble brigand. P2 and P3 discard OE, Hovel.
P2T1: Stonemason/Masquerade/Watchtower. Draws Necro, Masq, Watchtower, 2 copper
P3T1: Stonemason/Procession/Fortress. Draws necro, 2 copper, Fortress, Procession
P4-6T1: ---
P1T2: ---
P2T2: Play masquerade, pass watchtower. (P3 passes copper)
P3T2: Win.
Now, how exactly do you win?
1. Procession fortress, drawing stonemason, OE, trash the fortress for a catacombs into a fortress into your hand, and the original fortress in the hand too.
2. Stonemason on the fortress, get develops on the deck.
3. Fortress draw a develop. You now have 4 actions, watchtower, fortress, and develop in hand.
4. Keep developing fortress into a develop on the deck and a fortress in the hand through catacombs until all three piles are empty.
5. Buy an estate.
You can certainly do more than this, but here you go.