I looked it up, and PoE only accepts six players. That's... actually probably more than sufficient, but it's a game with some continuity (because level and equipment matters), and is a big download. Probably not ideal, but if a lot of people want it, I guess it's good.
Space Station 13 would be very entertaining. I ghosted in a round a year or so ago, and watched a boarder murder half the crew with an SMG. Though, problems would be the relative length of a SS13 turn, and the menagerie of things that need to be taken care of. When I archived binged the SS13 wiki, I was amazed at just how much stuff there was to do to keep the station functional. If only a few people are veterans of the game, I could see the whole thing going to hell quick, even without the normal challenges that come up. Maybe that's a good thing, though.
Edit: Also, Apparently there's a mod that reliably allows you to connect to specific people in Dark Souls. I still would love to do a fight club in it, or even some sort of coop challenge. "NG+7 perma-gravelorded aggressive mod" would be suitably challenging, I imagine.
I believe there are planet-type maps these days that don't require so much upkeep as a station to keep running. Otherwise, yeah, there's a little busywork at the start to keep things going smoothly (such as setting up engine). For an experienced mod though lots of options for custom rounds are available.
I like the concept of Zombie Master, and apparently there's a Zombie Master 2? I dunno how well it works in practice, but it seems good.
The sequel has a stable build, but is rather incomplete compared to the original. Better stick to the forst one.
I thought of PS2, but any time I've tried to play that with other people, I didn't really feel like I was playing a game with them. More, I was in a battle that they were also in, somewhere, and I might occasionally run into them. Maybe it'd be different with more people.
That's cause you try to play it right. The most fun I've ever had with PS2 is me and a buddy grabbing a quad, setting a waypoint deep in enemy territory and racing over there, trying to survive as long as possible. Or daring to see who can run the most circles around an enemy tank before blowing the fuck up. Or getting into an enemy base and ramping EVERYTHING. Or grabbing fighters and jousting with each other. Or 1 person in a quad, the others in planes, and then the airplanes have to try and ram the dude on the quad who tries his best not to get crashed to hell.
Also, I think team fortress 2 has a PvE mode these days. Some other f2p online shooters have PvE modes as well, often defense maps, so those could be fun to try. Oh, and the spring engine is free and fun, though isn't very good for beginners.