His girlfriend?

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I met a guy (2 weeks ago). I like him, we have chemistry together. He seems to like me too.

BUT (!) he has a girlfriend (of about 2 years, thanks fb), he's living with her.

He never mentioned her, I know this thanks to online stalking.

Normally I'd let him go, but I feel like we really have a connection and I'm willing to do something, but I don't know what. I'm not expecting him to leave his girl right away, because he met me and we like talking to each other. But I'd like to push a little further and see how it goes.

What do I do?
We're friends, nothing but friends. But we get along really well and I wish for something more.

Obviously, it's all up to him, he's got a decision to make. I'm just asking what to do to increase chances of choosing me.