Coop games with more than 4 players

Rust, DayZ, Hurtworld, WoW etc.

Friday 13th = 8 players
Deceit = 6 players

Human: Fall Flat
Robot Roller-Derby Disco Dodgeball
Insurgency
Wurm Unlimited
Take Thy Throne (at least i think)
Death Toll (something like PUBG - in closed beta, if will you be lucky you will get acces)

Arma 3.

The Red Solstice

I'll add Terraria and Don't Starve to the list. Both can be played as co-op or PvP.

Rainbow six siege!

Sven Coop

If you're up for aRPGs like Torchlight 2, definitely check out Path of Exile. I don't remember the party limit, because I've only ever played with 3, but I am pretty sure it's more than 4.

Right now, the only others I can think of for so many players are PvP play games like Runbow.

Dead by Daylight allows you to play with 3 friends (4 survivors) against one dude, the killer... and I think the killer can be a friend too.

Killing Floor 2 and Path of Exile

castle crasher , Dont Starve Together

you can use cooptimus to filter games with any categories you want, far easier than asking others. =3

What do u mean by co-op, online co-op or split-screen co-op?

Sonic & All Star racing transformed

Starbound (maybe you need to edit some config files), Path of Exile (up to 6), Broforce (up to 4 unfortunately)

Town of Salem is good for big groups and it's technically FTP if you go to their website instead of steam. But even on Steam it's only a few bucks and you get some cosmetic stuff free.

Tabletop Sim

Talisman
http://store.steampowered.com/app/247000/Talisman_Digital_Edition/

No More Room in Hell can be played by up to ... um ... I think 8 players. It is also free to play. It is rather slow zombie game where you have to either defend areas or do mission objectives. Animations look sometimes a bit clunky, especially third person. But as you can get surrounded easily the game has some emphasis on team play and coordination.

Not sure how it is today but you should avoid joining unlimited ammo Servers which have been implemented against the wishes of the developers. It goes against the complete design and basic idea of the game. So try to play it the way it was intended to also if it means dying a lot.