Currently the closest thing to what you're looking for is the Captain mode, which is 5v5 (or 6v6, can't remember) and you control a small group of 10 or so soldiers each. It's plagued by balance issues at the moment but it has a community that absolutely love it, and it should be improved with time.
Arguably one of the most popular modes from the previous title is the 'Battle' mode which can be up to 125v125 real players, however it is not currently in the game and noone is really sure what they plan on doing with that.
There are, however, mod teams looking into these sort of things and a campaign co-op mod is in the works already, which should scratch the itch for what you're looking for if it all goes well. All in all, I'd say don't get too excited for MP at the moment, it's in a very bad state but if everything works out then it should be great.