One per player.
The text of rule 700.8 makes this clear (emphasis mine):
700.8. Some cards refer to the number of creatures in a player’s party. A player’s party consists of up to one creature that player controls for each of the following four creature types: Cleric, Rogue, Warrior, and Wizard.
Throughout 700.8, the party is always referred to in a one-to-one relationship with the player. A player has exactly one party (even if it's empty); phrasings like "a player's party", "that player's party", etc. would make no sense if they could have more than one.
Despite the common meaning of "party" and the flavor it evokes, party is not a mechanic for grouping creatures into discrete entities, it is a count maintained by the player who controls those creatures.