I confirmed that 3 teams conquest is currently possible, but there are caveats.
The game gets confused about what game mode you are trying to play, so it enforces the lower max bot limit of 36 bots total, instead of 64.
AI for team 3 behaves more like tdm than conquest, so you have to give it more goals to keep it focused on the game objective. The AI commander for team 1 and 2 still works properly and gives conquest-type gameplay commands, but team 3 doesn't get objective orders from the AI commander, so you have to do it manually. Even after creating the typescript variables and arrays for AI commander to interface with a team 3, I think the game's code just doesn't expect/try to interface that way.
There are only 2 team outfits and vehicles, so team 3 is going to look like an existing team. Not that most would really notice.
It works, but who would play it?
But Battlefield 6 needs to be updated again for a mode like this. For example, the game mechanics are too fast; they need to be slowed down a bit. The game mechanics should be the same speed as Battlefield 1. Otherwise, three different armies fighting each other on a very crowded server can become unplayable. The fast pace of Battlefield 6's mechanics already makes it unsuccessful and unplayable for Battlefield fans. Therefore, Battlefield 6 should avoid imitating Call of Duty and make the game worthy of Battlefield.
