Ok, what I'm thinking is, and keep in mind this up for modification....

We are in the future... perhaps 20 years from now. Between the present and then (we'll say 10 years ago), Animus tech grew a lot and kind of became a household staple, based on how far along they were with it in Black Flag (headset). Subsequently, it ended up being banned by all world governments. They couldn't have people looking back at the past and discovering their secrets, the Templars being exceptionally afraid. If you were caught with one, you'd be imprisoned.

SO, 10 years after that we have our characters. Somehow they have gotten their hands on an Animus headset, perhaps two sets. They use them to go back to present time (2014), or early 2000s, later 2000s, or even around the time the tech was banned. They investigate current, near-past, or near-future events/conspiracies. 

I want there to be some ultimate goal in mind, and that's where the collaborating comes in. I figure placing them in the near-past/present/future enables us to not have to put too much research and effort into our conspiracies, assuming we're all up to date on current events. Obviously a good one might be something like 9/11. It also enables us to create our very own near-future conspiracies. So I think there's a lot of wiggle room there.

If anyone is interested in going further into the past, I'll listen to the idea. Obviously we have plenty of time to go over multiple time periods, if we want. However, I will not do time periods that have already been accounted for in the game.