In a 2-player game, respecting the 3-pile rule, I can get as high as 255 (51 Tactician plays):
Kingdom: Black Market (containing Masquerade, Throne Room; or those can just be in the Kingdom since there's room), Highway (or other cost reducer), Royal Carriage, Tactician, Hireling (or other duration draw), King's Court, Prince, Inheritance, Pathfinding
Empty Piles: Prince, Tactician
In play: Hireling x9
Set aside: Prince x10 with King's Court x9 (courtesy of Highway) and Throne Room x1; Royal Carriage with Inheritance
Tokens: +Card on Tactician, Inheritance with Royal Carriage
Tavern Mat: Royal Carriage x8, Estate x13 (7 from the Supply, 6 starting Estates courtesy of Masquerade)
Hand: Tactician
Start of Turn:
1. Resolve Prince A, playing King's Court A, playing Tactician A three times (drawing a card each time with Pathfinding to discard with Tactician). (Total plays: 3)
2. Resolve Hireling A, drawing Tactician B.
3. Repeat 1-2 eight more times. (Total plays: 27)
4. Resolve Prince J, playing Throne Room, playing Tactician J twice. (Total plays: 29)
5. Call all of the Royal Carriages and Estates, playing Tactician J twenty-two more times. (Total plays 51)
Next turn, you draw 255 cards from your 51 Tactician plays.
You can get even more with Procession and Lurker/Graverobber/Rogue (for example, replace Throne Room with Procession, use some Caravans or something to draw a Lurker and a cantrip, then during your Action phase use Lurker to get the trashed Tactician back, draw it with the cantrip, and play it), but I haven't optimized it.
Edit: Overlord could also help here. Or instead of Kinging/Throning/Processioning the Tacticians directly, Throne a Vassal/Herald and have it hit King's Court (or Procession) for the Tacticians. I bet you could get a really high number with an elaborate enough setup, using Prince-based chains to play most of the Tacticians at the start of your turn where you can use any number of Durations (or Guide) to get more cards after discarding with Tactician.