I've had this happen a few times now in the past year and I think a lot of guys will deal with this kind of thing as they improve their lives and start actually approaching.

The girl below me in my apartment building shows a lot interest when I speak with her, but cools off via text. She has told me she has a boyfriend and I can't get her to come hang out on a date. Last night, though, she came up with cookies and we chatted with a lot of mutual interest for about 15 minutes before she brought her boyfriend up (in conversation). What is the right way to proceed with girls in close living proximity that have boyfriends? Should I be throwing some light, but direct sexual compliments her way? Should I just try to kino? I want to make it sexual, but I don't want to creep out my neighbor who is being friendly and giving me cookies at 2am.

EDIT: To those who say don't proceed, does that mean stop hanging out? Isn't there a good way to keep the sexual tension there, but repressed, until they inevitably break up.

EDIT 2: My goal is not to break up the relationship or to even have her cheat on him. I just want her to know that I'm an option and a damn good one. I do believe in fidelity.