Since it's for the purpose of streaming, GTAV is hands down the best I can think of. Though it might be fun to watch you guys play CS:S or CS:GO, L4D2 Versus maybe. Killing Floor 2, also Arma 2/3, especially if people are inexperienced, it could be fun to watch the horror, trying to figure out what's even happening :D
Quake Live is an ok choice. Left 4 Dead/Left 4 Dead 2 as was suggested above is also a good choice. DogFighter is a decent little aerial combat game that might be worth a try. Another solidly fun game is Awesomenauts:
It's a great 2d platforming multiplayer game. It's sort of a map control/capture the flag type game with stat based power-ups. It's good fun.
Just Cause 2 Multiplayer would be a more ridiculous choice:
It's essentially GTA Online, except with a game more suited to the batshit insane things that will go on.
And lastly, Mount Your Friends is almost disturbingly fun:
If you want something truly ridiculous to stream...
I'd add PayDay: The Heist into the mix as it still has the appeal of the PGP team working together to do a heist, as per PayDay 2 but with a slightly higher chance of them staying alive and with the earlier forms of drilling and securing the loot (etc). However, either would be good to watch.
Also, gotta do an MMORPG at least once. Star Wars and Star Trek would have to be high on the list - nerds nerding out? Yes please.
Oh oh. Hammerwatch, old school 4 player dungeon crawler in 8-bit style and difficult. Or Full Mojo Rampage a modern 4 player dungeon crawler still pretty difficult.
Both fun multiplayer games, Hammerwatch has lots of secrets hidden behind cracks in walls and buttons for extra stuff to do, some puzzles typical of the genre. You pick classes at the start somyou can chose how you want to play. And if you complete the main story dungeon there is steam workshop user created levels.
Full Mojo Rampage has items to power up you character and customisations on how they look and perks for the caharacter so.you can build a team or play how you like fighting style wise. Modern zommed out 3D dungeon crawler.