The official AoE3 website claims you can play "multi-player campaigns":
Play against your friends
There are several multi-player campaigns where you can get into some heated battles with your friends.
However, the only campaign I've found in the game was the single-player one. The very "Campaign" menu option is only available after you click "Single Player" first.
There are multiplayer scenarios, but I don't think they mean that. The game itself distinguishes between "scenario" and "campaign", so does the official website, I guess.
So what are "multi-player campaigns" and how do I play them? I use "Age of Empires III: Complete Collection" from Steam.
Best Answer
There are no built in multiplayer campaigns within the game. If you want to play multiplayer campaigns, you will have to download them from 3rd party multiplayer campaign providers.