Sorry, but I have to be completely honest here: That would be a really cheesy idea for a ME4 protagonist. I wanna be able to play as both Asari, Turian or whatever but if the backgrounds I can choose from all have to do with Shepard and his LI it's anti-immersive, fanservice and just plain cheesy. I wouldn't want that.
One thing they did with ME2 and ME3 that I didn't like so much was keep faces from ME1 reappearing conveniently in different missions, like Nassana being in Thane's recruit mission, Harkin being back in Garrus' loyalty mission to ME2 squadmates being conveniently set on the same site Shepard lands on in the ME3 side-quests and stuff like that. The reason why I dislike that is because ME1 made the universe feel grand and incredibly big in scope, even reinforced by the somewhat empty terrains of random planets where you drove around in your Mako. It gave me moments where I could just sink in how alone and little my character was compared to how large the universe was, but in ME2 and ME3, by constantly shoehorning in returning characters at every junction they make the galaxy seem small.
I don't want that. They say ME4 is gonna be more about freedom and exploring the galaxy as you wish to, sort of like DA:I's focus on exploration and open-ended areas. If they truly want to focus on that, stop intersecting the characters all the time. I don't even want to see Liara, unless Bioware realistically puts her in a position that makes her growth seem believable, like if she's somehow recognized as one of the main heroes who beat the Reapers but is now 300+ years older than before and resides at some... IDK, publically known as a representative for something... I don't know, maybe a war museum? (thank god I'm not a writer).
Intertwining stuff to characters we knew in ME3? No. Making us play as the direct offspring of Shepard in ME4? No way. Just no friggin way. It would cheapen the expansiveness of MEU.