The Mutiplayer can take place in almost anywhere, at almost any given moment in the ME canon.
Actually - if you think about it, some aspects of MP don't make much sense relative to SP - particularly the enemy types.
The collectors were presumably wiped out in ME2, so their presence in ME3 MP is questionable. Fighting Cerberus post Cronos has similar issues. Late in the SP campaign, the geth could be your allies, though I suppose there may still be some pockets of enemy geth. Reaper enemies make sense throughout ME3, but not before.
That being said, taking place in Andromeda presents very few risks for the Multiplayer. The same is unlikely to be the case of Singleplayer.
At the very least, I would expect different sets of enemy factions, and of course new maps. Maybe some new kits based on new species, and different weapons. Aside from that, I'd expect they would not want to make a lot of changes to something that has been very popular and successful thus far.
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The description in the 'leak' sounds like a decent way of integrating SP and MP - where the player can assign resources to accomplish a task or go into MP to play through the task directly. I just hope they don't gate any SP content behind some MP requirement, as it tends to stir up hard feelings on both sides. The only possible benefit is that it can get people to try MP who would not otherwise check it out. The downside is that SPers feel like they have to play a game mode they don't really want to play, and MP teams end up having to accommodate players who really don't want to be there.