Well... what do you mean by "canon"? I mean, if you go by what's actually canon and in the game, the romances you have are:

Phoenix/Dahlia (in the past)
Gumshoe -> Maggey (which she might return)
Diego/Mia
Ron/Desiree

And obviously people ship a whole lot more than that. Nick/Edgey, Phoenix/Maya, Franziska/Adrian, etc... none of those are canon. But they're still hugely shipped (even if personally Phoenix/Maya kinda squicks me out :/)

Personally, though I do like to have a possible BASIS in canon, sometimes it's just I think that two people would work really well together. (For example, I think Franziska/Maya would possibly be one of the cutest things -ever- and they, uh, don't even interact much at all.) I'll be honest, I can't see Edgey/Maya (Maya in a serious romance with ANYBODY is sort of "do not want" personally, which is why my take on the aforementioned Fran/Maya is almost closer to a good friendship/very lighthearted as opposed to anything else) but sure, you're totally welcome to ship it~

But yeah, I got a bit sidetracked >_> I don't think everyone just follows "canon", not at all.