I've taken this from the activity feed that I posted back on the 24th so people can get a good idea about the possible games that multiple people could play. Anyone who reads this can be invited, not just the usual group of friends. I'd recommend making an account with Skype for online chat. I've included a list of possible games we can play, feel free to comment and lets see what kind of a selection we can get.

Alien Breed 1,2,3 - 2 Players
Alien Swarm - 1-4 Players - Free to Play
Borderlands 1 or 2 - 1-4 Players [bandit]
Counter-Strike: Global Offensive - 1-24 Players, servers may vary [csgocross]
Dead Island - 1-4 Players
Dungeon Defenders - 1-4 Players
Far Cry 3 - 1-4 Players Multiplayer mode
Galactic Civilizations II: Ultimate Edition - 1-8 Players
God Mode - 1-4 Players
Killing Floor - 1-24 Players, Servers may vary
Left 4 Dead 1,2 - 1-4 Co-Op, 1-8 Versus
Marvel Heroes - 1-4 Parties, Free to play MMO
Orcs Must Die! 2 - 2 Players
Path of Exile - 1-6 Players, Free to Play
PlanetSide 2 - 9001+ Players
Portal 2 - 2 Players [p2turret]
Ragnarok 2 - 1-4 or 5? Parties, Free to play MMO
Santum 1 or 2 - 1-4 Players
Section 8: Prejudice - 1-4 Players. Horde Mode
Shoot Many Robots - 1-4 Players
Sid Meier's Civilization V - 1-16 Players, Team Modes
Spiral Knights - MMO, 1-4 Parties
Team Fortress 2 - 1-6 Players MvM or 1-24 Players, Servers may Vary. - Free to Play [sentry] [sticky] [medicon]
Ticket to Ride - 1-4or5 Players
Torchlight 2 - 1-6 Players
Warhammer 40,000 Space Marine - 1-4 Players Horde Mode