So if you're familiar with the Left 4 Dead franchise, I'm sure you'll be well acquainted with the Versus Mode. If you're not familiar with those, this will be a bit harder to wrap your head around, but it isn't too hard to understand.
Basically, imagine a game where a group of players controlling a set of survivor/human characters that have to reach the end of the level. Their progress would be impeded by a team of opposing players playing non-human characters (these would be the zombies in L4D). This is all well and good, up until a THIRD team appears that is attempting to destroy the human characters before the other non-human team can, racing to do more damage than the other while the humans attempt to survive the onslaught. I would say that resources wouldn't be as scarce in this game compared to L4D, given the increased danger from facing two opposing sides at once. This is done to prevent players from getting bored or overly frustrated while playing the human characters. The humans would have to be armed enough to take on the opposing non-humans without being too powerful to kill.
Thematically, I imagine this in a sort of 'Rogue Robots vs. Invading Aliens vs. Humans' scenario, which opens up a lot of possibilities for both human interaction with a variety of weaponry, as well as a good selection of non-human classes and tactics for both killing the enemy team and destroying the human team. For example, I had an idea for a level that ends up passing through a robot factory of sorts. The humans burst a hole into the side of the factory, which activates an objective for the robots to defend a generator in the center of the room. The aliens would obviously want to attack that generator for a major point bonus, and because it is also in the humans' interest, the two teams would become temporary allies until that objective is complete. The robots would be compensated with a massive upgrade, either in the form of a swarm of lesser robots or in the form of a special character that is more powerful than the others, like a gunship or a giant mech. This helps create more variety in the levels and breaks up the monotonous "Humans go to point A, monsters stop them" game type that this is inevitably going to inhereit
Anyways, I'll stop rambling. Tell me your thoughts and questions down below~