He has a girlfriend.
If you were someones girlfriend, would you appreciate another girl asking about how she can get to know him better?
First rule of girl club is leave other girls boyfriends alone.
Second rule of girl club is leave other girls boyfriends alone.
If he breaks up with his girlfriend on his own, having nothing to do with you, then talk to him.
Next time your alone on the elevator with him, ask him how his girlfriend is. That way he knows your on to him.