Should be possible on turn 1 with one player in classic empty the supply fashion:
Events: Travelling Fair, Advance
Kingdom: Possession, Pooka, Tracker, Fortress, Doctor, Blessed Village, Priest, Watchtower, (two extra slots)
Starting hand: Cursed Gold, Pouch, Copper, Copper, Necropolis.
Play treasures in hand to have $6+2 Buys. Buy Travelling Fair to have $4+3 Buys.
Advance Necro into Fortress, topdecking.
Buy Doctor, overpaying 1 and trashing the Fortress on top.
Advance Fortress into Villa.
Play Villa to have $1+1 Buy. At this point, our hand has only a Fortress. For the rest of this solution, when we buy Advance, it is to trash a Fortress in our hand.
Every time we Advance into Villa and play Villa, we gain $1. We do this 3 more times, starting a buy phase with $4+1 Buy. (At this point, we have used 4 Villas total.)
Now, buy Travelling Fair twice to be left with $0+3 Buys. Advance into Priest, topdecking. Advance into Blessed Village (not topdecking), taking the boon that gives +1 Card to draw the Priest. Advance into Villa.
Play Villa and Priest, to have $3+1 Buy. At this point, if we buy Travelling Fair then Advance, we'll stay at $3+1 Buy. We can do this repeatedly to put Priest, Priest, Priest, Priest, Fortress, Watchtower, Watchtower on top of our deck (in an order that Watchtower ends up on top). Finally, Advance into Villa. (At this point, we used 6 Villas total.)
At this point, we have $3+0 Buys. Play the Villa, then the Fortress, drawing Watchtower. Play the Watchtower, drawing Watchtower, Fortress, and 4 Priests. Play the 4 Priests (we have enough actions from all the times we played Villa earlier in the turn). Now we have $32+1 Buy.
Now we have 5 Priests in play with Watchtower and Fortress in hand and we can go to town. This would already be enough to empty the supply if it weren't for the cards with Potion in their cost. To also clear all 10 Possessions, we need to draw and play some potions at some point. We can do something like TF + buy/trash copper several times to build lots of money, Advance into/trash the remaining 8 Fortresses, then buy and topdeck something like (Pooka Copper) x 2, Potion x 10, then gain Villa, play 8 Fortresses, 2 Pookas on Copper to draw all 10 Potions and go back into our buy phase.