Is there a local pc game that can be played with more than 4 players?

While 4 is consider the "local ideal" with a single PC, there are games that will go beyond that point.

HOWEVER, this generally requires some extra hardware… Like another PC or devices to handle it.

Jackbox Party games generally require all players to have a smartphone OR a tablet to play through their web browser (as the PC serves as the "central screen"). These games generally support up to 8 main players with excess (or those entering late) becoming "The Audience".

Other games line Minecraft do have LAN play as well, but requires one PC per player.

A little extra research (generally through Steam's catalog) will find a general selection of multiplayer games that you can pair down from there.