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[hider=General Outline]Phase I: 
The Enterprise finds themselves in a completely different region of space. No formality at all. They pick up the escape pods faint signal and one life form on board (Rommie - Android - doesn't have a life sign as she's an android). They pick up the two.
Now because the Andromeda Ascendant is familiar with the tri-galaxies (even though this is a different universe) Rommie's able to pick up the fact that they are in the Andromeda Galaxy. 
So the Enterprise needs her initially as (though slightly different due to the universe) she's familiar with the stars in this region.

This phase really they're transitioning through Andromeda Galaxy as they try to find a way that can get them back to the Milky Way.
The Enterprise crew thinks this is their universe (they don't suspect otherwise) and the Andromeda crew isn't sure what's going on as the systems they go that are major Commonwealth systems have no presence in them. 

This phase technically ends when they discover the Andromeda Ascendant (ship) and the fact that slip stream still works.

Phase II:
Reunited with herself, Rommie and Gaharis works with the Enterprise crew to somehow do temporarily connection of the two ships to travel the slipstream.
Basically this phase is the journey back to the Milky Way.
Slipstream is an interesting method of hyperspace travel. The more a route is traveled and mapped - the quicker it is to navigate (and safer).
As this is a completely different universe, even though they know the routes it takes them longer.
Not to mention by this time we would have introduced other races that can and might be a threat.

Phase III:
Back in the Alpha Quadrant, we find we are in the Trek universe.
The Andromeda has to figure out what to do now. This isn't home but at the same time, can they get home? Or will there even be home for them?
(Remember they left at the beginning of the war. Gaharis will be fairly confident his people would have won by now so Andromeda going back would only end up in her being destroyed - possibly. Not that it will stop her lol).

Really, by this time we can have an idea of what we want to do. Does the Andromeda stay? Does the Enterprise work with them to find a way back?
Does the enemies from the Andromeda galaxy become a major threat to the Alpha Quadrant and both ships are needed to help keep the Milky Way safe?

There's a lot of possibilities I can see here. But this is WAY down the line.
Pending how we do it, we can also have this phase end with the destruction of the Andromeda Ascendant leaving Gaharis and Rommie left. Both could join up with the Enterprise and we can do adventures this way :)[/hider]