Possible to make Xbox One and PS4 work well on a large network behind a NAT firewall?

So I see this question a lot from the perspective of college students in dorms who can't get multiplayer games working because of strict NAT conditions on their dorms network.

I have been trying to understand this topic from the perspective of one involved in managing such a network to see if there is a way we can improve the situation, either by some limited changes to our network setup, or by having a simple recipe for our users to get their systems working.

What I am seeing is that the consoles need to have ports mapped to allow incoming connections to reach them. I can't see any reasonable way to allow this for say 200 Xboxes all sharing a couple of outside IP addresses. Even if we could allow UPNP wouldn't each xbox try to map addresses for itself and break the previous persons setup?

Thanks