My first attempt:
Kingdom: Black Market, King's Court, Throne Room, Ambassador, Cultist, Rogue, Governor, Tactician, Golem, Doctor
Black Market deck contains: Watchtower, Hermit, Caravan, Rats, Fortress, Haven, Candlestick Maker, Wharf, Torturer, Council Room, Soothsayer, Horse Traders, Masquerade, Lighthouse, 10 Lab variants (being able to draw a Golem and whichever other card is good enough)
Use Shelters, no Colonies.
6 players. (EDIT: Doesn't actually need 6 players, 3 should be enough)
Player 1 buys a Black Market and gains the Hermit. Later, he also buys 9 Rogue and uses those to gain all the Madmen (just because I'm too lazy to make sure that he actually has enough +cards and +actions to pull everything off without them). He also buys 9 King's Courts, 8 Throne Rooms, 3 Cultists, 10 Ambassadors and 9 Governors.
Player 2 buys a Black Market and gains the Lighthouse, the Masquerade, the Torturer, the Council Room and the Soothsayer. He also buys 1 Throne Room and 1 King's Court.
Meanwhile, Player 3 buys a Black Market and gains the Watchtower, the Candlestick Maker, the 10 Lab variants, the Wharf, the Caravan, the Horse Traders, the Fortress and the Rats. He also buys a Potion and buys all of the Tacticians and 9 Golems and 6 Cultists. He also plays the CSM over and over, gaining 5478547694869 coin tokens, and buying as many basic cards as is needed without ending the game.
Then, the following turns happen:
Player 3:
Play Golem, finding Tac and a Lab variant, play Tac first, then the Lab variant, which draws a Golem and a random card.
Play Golem, finding Tac and a Lab variant, play Tac first, then the Lab variant, which draws a Golem and a random card.
Play Golem, finding Tac and a Lab variant, play Tac first, then the Lab variant, which draws a Golem and a random card.
Play Golem, finding Tac and a Lab variant, play Tac first, then the Lab variant, which draws a Golem and a random card.
Play Golem, finding Tac and a Lab variant, play Tac first, then the Lab variant, which draws a Golem and a random card.
Play Golem, finding Tac and a Lab variant, play Tac first, then the Lab variant, which draws a Golem and a random card.
Play Golem, finding Tac and a Lab variant, play Tac first, then the Lab variant, which draws a Golem and a random card.
Play Golem, finding Tac and a Lab variant, play Tac first, then the Lab variant, which draws a Golem and a random card.
Play Golem, finding Tac and a Lab variant, play Tac first, then the Lab variant, which happens to be Scrying Pool that draws a Tac, a Necropolis, a Wharf, a Caravan and a Haven,
Play Caravan, Haven, Necropolis, Wharf and Tac.
Player 1:
Play 10 Hermits.
Throne -> KC -> KC -> Ambassador (reveal and return 1 Cultist every time, Player 2 is protected by the Lighthouse, Player 3 reveals Watchtower to draw +9 cards) -> Rogue (gain the three Cultists) -> KC -> Governor (draw the Cultists, P3 draws +3 cards) -> Ambassador -> KC -> Rogue -> Governor -> KC -> Ambassador -> Rogue -> KC -> Governor -> Ambassador -> KC -> Rogue -> Governor -> KC -> Ambassador -> Rogue -> KC -> Governor -> Ambassador -> Rogue -> Governor -> Ambassador
Throne -> Throne -> Rogue -> Throne -> Governor -> Throne -> Ambassador (return 1 Cultist every time) -> Throne -> Rogue -> Throne -> Governor -> Ambassador
Rogue
Governor
Throne -> Ambassador (Player 3 reveals Horse Traders now)
Discard everything, shuffle, draw at least 3 KC and something else
Player 2:
Necropolis
KC -> Masquerade, pass whatever cards, receive 1 KC and 2 Governor from player 1
Throne -> KC -> Council Room -> Soothsayer -> Governor -> Governor -> Torturer
Player 3:
Don't play a card, just spend your tokens and overpay for a Doctor, trashing 6 Cultists, 1 Rats, 1 Fortress and 1 Overgrown Estate.
If I'm correct, now Player 3 should have
5 (original hand) + 5*10 (Tacticians) + 7*3*3 (KC'd Ambassadors) + 3*2*3 (Throne'd Ambassadors) + 8*3 (KC'd Governors) + 2*2 (Throne'd Governors) + 1 (regular Governor) + 3 (KC'd CR) + 3 (KC'd Soothsayer) + 3 (KC'd Torturer) + 1 (HT) + 6*3 (trashed Cultists) + 1 (trashed Rats) + 1 (trashed Fortress) + 1 (trashed OGE) = 196
I'm not sure if you can draw more cards if you just give P2's Throne and KC to P1, and there might be other room for improvement too.
EDIT: Removed the thing with Swindler since it literally just made things more confusing.