No. I really like everything about a great majority of the NPCs and having them run off on some random, non-canon romance with anyone and everyone would be an insult to their characters and personalities in my opinion. I can't comprehend anyone having any genuine interest and respect for the characters they claim to like when they want to meddle in their story like that. They just enjoy the aesthetics and little more as far as I can tell. If they added some new characters created explicitly for developing relationships with(of varying degrees) then that'd be one thing, but not existing characters.

Kikoten's suggestion about a one time, non-meaningful date where you get to explore a character's backstory a little bit however.... that sounds good.