The only problem with that being that Briar's never serious about girls, he's just looking for a fling, and from what we've seen of Daja, she's not one to fool around for kicks and giggles without it being serious. So if Daja was really interested, I can't see Briar doing anything other than backing off.
Plus, arguing over someone else/liking the same person has the other problem of you're leaving the other person's wishes/desires out of the equation entirely, which doesn't seem like Briar or Daja to me either.