I've done quite of few head to head campaigns throughout the total war series, and they are quite fun. working together but also fighting other people in the same campaign, even if we work together at times you still fight and take over each others provinces in a head to head, seeing who is better in the campaign and in battles.
Anyways to get to the point head to head is quite fun and it would be even cooler if we could have another player, in a campaign head to head, now I can already imagine some comments being like but like that would take forever to play and finish. Well, I would say you could make it so you have the option to simultaneous turns like they do in civilization when all player end/play their turn at the same time. If that doesn't work, there are still turn timer, and even if its a bit long the players who think that do not have to play a 3 player head to head, it doesn't affect them, me personally wouldn't care about the wait, or would rather have the option to wait, then be just limited too two players in a head to head campaign.
I'm no programmer but I don't think it would be that hard to include this in game, you just have to create the option for another player to be in a 2 player campaign, it doesn't seem so difficult to do, I could be wrong, but I think its little effort compared with the coolness of three players multiplayer campaigns.