Okay so, assuming that the ending was meant to be taken in a literal sense, and not in the super tempting and cool indoctrination theory way, the sequel would play out IN DRASTICALLY DIFFERENT WAYS DEPENDING ON THE ENDING YOU CHOSE. (That is the only way that the terrible ending in ME3 could possibly be forgiven).
FOR THE DESTRUCTION ENDING:
Here you would be able to create a totally new character with the ability to play as any of the races. The story would be about the immediate after-math of Commander Shepard's crazy ass decision to blow up the Mass Relays. Depending on race that you choose to play as different stories will play out, with the overarching story being a large scale war between the races erupts with the Reaper threat gone. The war of course is over who gets control of Earth. If you are a member of one of the species who can't consume the food of humans, your first task is to kidnap as many scientists as possible, preferably Salarians. As one of the races who can consume human food you are faced with the choice of trying to push for your race to co-exist with the humans or annihilate them knowing that the resources on Earth couldn't possibly support two races. Either way there's probably going to be a ton of cover-based shooting involved.
FOR THE CONTROL ENDING:
You continue living as "Shepard", some kind of almighty being that is in control of the Reapers. After being assimilated into the crazy hive mind that seems to make up the Reapers you discover other beings that are separate from yourself yet part of the same mind. Unfortunately despite the Reapers being shown as leaving Earth at the end of the previous ending it was only temporary as Shepard managed to gain complete momentary control of the Reapers since he was an unexpected force within the hive mind. However, now the other beings within the mind have become aware of his presence and control has become split amongst the beings. With only Shepard's will against the total destruction of life, the majority of the Reapers soon continue the mission of destroying all sentient life in the universe. Here Shepard's goal is to traverse this digital realm and take out the other beings through some method that should be thought up of by Bioware before it's too late.
FOR THE SYNTHESIS ENDING:
The game consists of you living in the new planet Joker discovered. The gameplay is a quicktime event where you have sex with EDI and make half-robot half-human babies cause that was the whole point of this ending. After that scene the camera zooms out and the rest of the game takes as a sort of city building game with Joker as mayor. Your job is to build a civilization with the initial goal being to first achieve travel into space, followed by the creation of a system similar to the Mass Relays. Along the way of course your other crew members (who survived) also have their own babies that are obviously different species. The challenge is then to try and achieve your scientific goal, while at the same time keeping peace among the growing population of different species with different ideals. Of course, there's also the problem of potential native life on the planet. etc.
Of course all of these game stories/types would be included in ONE SINGULAR GAME that is developed by Bioware and handed out for free to all those that suffered through the ME3 ending.
I can't believe I typed all that just because I was bored, and probably no one will ever read this post since it's like on the third page and I haven't quoted anyone. xD