Very basically, two possibilities...
1) Given the normal relatively slow movement of PbP games, we run two different teams, and while everybody else has a character on each team, we as GMs only have one character, on the team we aren't running.
2) Second, the first GM runs a scenario to a finish, then the other guy takes over, to run a scenario of his own.
As far as the action is concerned, its still a big bad universe out there. The Reapers are no longer a threat, but a lot of worlds have been ravaged, and are in the process of rebuilding. Some Krogan have headed home to take part in the rebirth of their race, but not all of them are quite ready to give up the life of free wandering to take up the responsibilities of clan and race on Tuchanka.
The remaining Reapers are helping where they can in rebuilding, but that's not exactly their forte, so while they can offer lots of technological insight, the industry to build the things they offer has to be rebuilt before they can be of much practical help.
Given that nobody wants to see the Reapers as galactic policemen, just in case their new friendly/nice Reaper facade is fleeting, most militaries are deployed to watch the Reapers, assist in rebuilding, and guard core systems. The damage to the Mass Effect Relay network is fairly crippling to commerce, and to the Alliance as a whole, though of course the Reapers are helping as much as they can to get the network repaired as a priority.
The Citadel is still in the Sol System, though its been towed into a stable Lagrange Orbit. There is an ongoing debate about what to do with it. The thing was built as a deathtrap, millions of people died on it during the Reaper war, and many of its key systems seem to be inoperable, since the undefined but cataclysmic events that ended the war.
Chaos is everywhere, from the streets of Earth's ruined cities to the far corners of the the galaxy. Cerberus isn't dead yet, though its head has been cut off, and key assets are still out there somewhere. Pirates and local warlords are popping up anywhere that's not under the guns of a major task force.
There are rumors of rogue Reapers, who somehow missed or ignored the order to stand down, hiding in the depths between the stars, using their indoctrinated agents to further their aims, whatever those are.
Against this backdrop, the remaining special operatives that fought against the Reapers, under the command of Garrus Vakarian, are being tasked with the mission to go out into the universe, and do their best to keep the peace until order can be re-established.