I can get to 157 in a 6-player game (final hand size: 92).
Kingdom: Ratcatcher, Guide, Watchtower, Duplicate, Transmogrify, Cultist, Inheritance
Inherited Cultists.
Relevant Cards in Supply:
20 Estates (courtesy of blocked Ambassadors; note that it starts with 16 Estates in a 6-player game)
3 Cultists
Empty piles: Guide, Ratcatcher, Transmogrify (note that it's 6-player game, so it takes 4 piles to end it)
Relevant Cards in Deck:
14 Estates
6 Cultists
1 Watchtower
Relevant Cards on Tavern Mat:
10 Guides
10 Ratcatchers
10 Transmogrifies
9 Duplicates
At start of turn:
Call 10 Guides (+50 cards, 50 total)
Call 1 Transmogrify to trash Cultist->Estate (+3 cards, 53 total)
Call 9 Duplicates to gain 9 more Estates
Reveal Watchtower to trash all 10 new Estates (+30 cards, 83 total)
Call 1 Transmogrify to trash Cultist->Cultist (+3 cards, 86 total)
Reveal Watchtower to trash the new Cultist (+3 cards, 89 total)
Call 8 Transmogrifies to trash Estate->Estate (+24 cards, 113 total)
Reveal Watchtower to trash all 8 new Estates (+24 cards, 127 total)
Call 6 Ratcatchers to trash Estates (+18 cards, 145 total)
Call 4 Ratcatchers to trash Cultists (+12 cards, 157 total)
Note that this won't even end the game, as the Estate and Cultist piles will still have 2 cards in them.