You might also want to look into one of these "Games as a service"-style games, like
Destiny 2 or The Division (1&2).
They have a lot of team activities, either competitive (Player versus Player or PvP) or co-operative (Player versus Environment or PvE). And their "Raids" require a LOT of communication to complete.
But if you're an ET player who's in it for that objective-based teamplay, Splash Damage are about the only people still doing it.
There was a great, if short-lived game on the PS3 called
M.A.G (Massive Action Game) that took the objective gameplay of ET, mixed it with the progression system of COD and then chucked up to 256 players in the mix. That was
fantastic, if crippled by the specs of the platform and the control method. Still kinda bummed that it never made it to the PC.