"The supply looks the same to all players."
All players see the same piles and number of piles, the same number of cards in each pile, and even the same embargo tokens everywhere, and presence/absence of special piles like Prizes, Ruins, Spoils, etc. This got a little screwy with heterogeneous piles like Prizes, Ruins, and Knights, and especially Black Market, but it's still pretty regular. Any interactions with the supply are globally visible, and globally symmetric.
Messing with this would be very hard, but not impossible. The easiest would be making Embargo tokens remember which player played them, and not giving curses to that player. Pain in the ass with bookkeeping, but possible. Another idea would be to change the way Knights work: instead of 1 pile with 10 different cards, each player has their own personal supply pile of 10 of the same knight, and can only buy knights from that pile. I could see Guilds doing something with "Guilds" this way, but it would be very hard to balance and design around. I would only consider it if Guilds come with a built-in way to enter other players' decks.