However, I have noticed quite a bit of crossovers with the classes I've played. One of the Consular companion was directly affected by action taken by the Agent, and one of the Agent's companions turns up in the Knight story, for instance. In general there's a lot of NPCs that you run into on one side or another that play a part in other class/faction.
More specifically, Qyzen says he used to run with Braden and specifically contacts Mako during a class quest, and Kaliyo shows up on the JK's ship.
All the stories are basically concurrent. The endings are not.
For Instance, the Bounty Hunter occurs first, as he forces the resignation/kills the head of the Republic. He is then replaced. The rest are a bit of a muddle. While the Warrior is laying the smackdown on Baras,
the Jedi Knight is simultaneously smacking down the Emperor. Immediately after they defeat their opponents and the Warrior strolls out of the chamber, Thanaton addresses the Dark Council on his loss of the Kaggath, in which case the Inquisitor walks in and defeats him.
Time-wise, the Bounty Hunter happens first, while the Inquisitor is probably dead last, we can surmise.