Canon endings are not really necessary. They would make things simpler, sure - but it's not impossible to write a story that carries on where ME3 left off. I've said this before; ME4 could center around colonization of other galaxies, after the destruction of the war with the Reapers.
In Destroy - there would be no Geth, or other synthetics
In Control - we'd have Reapers as allies. Obviously, their importance and support would be greatly limited for the purposes of the story.
In Synthesis - Everyone would have a different texture map, and same as Control; we'd have Reaper allies.
And you could even throw in a subplot dependent on a Control, or Synthesis ending; where characters wonder if the Reapers are actually still a threat, and are actually indoctrinating everyone - for the IT fans out there.
Heck, you can even bring Shepard back for the game. If you chose Control or Synthesis, you can do something similar to the Lazarous Project in ME2. Just give us some story about how the galaxy needs Shepard back.
If you picked Control, you can build something similar to the Terminator - cybernetic endoskeleton, underneath living tissue, cloned from Shepard. The body would then be used as a conduit for the Reapers, similar to EDI.
If you picked Synthesis, make it a techn-organic body, and say you have scans of Shepard's brainwaves, and somehow that gives you access to his memories, somehow. Make it sound sciency.
In Destroy, you'd just be in the hospital, or something.
The core story can still be the same, across all 3 endings.
The only ending I can't see them transferring over would be Refuse.