Hi!
Coop mode is an established concept in gaming. I short, all joining players team up - they join the same side, playing against AI entities.
Coop mode-maps for doom3 shouldn’t be that hard to create, in theory 
Given that you, as a map-maker, can create and include monsters in custom doom3 map.
1a) Have two spawn-areas: Team A spawn in the bottom centre of the map. Team B spawn somewhere in a corner.
1b) Let team B spawn in a room with no exits. Create a trigger in that room. Anyone joining team B (entering the room) is killed within 20 sec.
1c) Create a trigger in the room. The trigger prints (on screen), for those that trigger the print: "This map is for coop-play only. You can only play it as a member of team A.
2a) Create a “goal” at the top of the map.
2b) When team A reaches the goal (whatever that might be - could be anything), the game stops and team A is the winner.
3) Add more monsters closer to the goal.
4) Finish the map and release it.
5) Load the map on a server. If possible, have the “Message of the day” print: “Hi! This is a coop-play server. You can only join one side.”
6) Let players join. The quick ones will join team A, and go for the goal. The poor ones can either join team B and die, or leave the server.
Suggestion: Let’s use the prefix “coop_” (coop_mapname), for all map that we create and release in this way.
// Loffy