Maximum number of parties in MTG
There isn't a card nor an entry in the rules that mention multiples parties, therefore the number of parties you can form is irrelevant.
Also, rule 700.8a state s

The calculation of the number of creatures in a player’s party is performed automatically by the game and results in a number between zero and four. Players don’t declare which specific creatures they control are in their party.

The party mechanic doesn't care about the individual creatures but cares about the diversity in your whole pool of creatures.