Is it a real OT3 (they're all in love together) or is it a threesome? Because the second is much easier. There are lots of different motives other than love that a couple might add a third person. They could be curious, spicing up a relationship that's gotten a bit stale, one of them could be having an affair with the third and rather than split up, the cheated on parter brings the third person in (angst potential).
If you really don't like that third person (Character C), rather than pairing up A & B and wondering why the hell they'd want C, how about pairing up A & C who are both attracted to B (whom you also like). That makes the attraction real for you and you don't have to go into why icky C is in the original pairing.