Hmmm intriguing...Jun reminds Sho of something he once had but lost?
I will kill myself laughing if the cat has no connection to Jun at all but merely came along for the ride and is now living in a penthouse.
Sho seems to have a lot of material wealth but not much in the way of happiness in his life, despite his friends. (Who incidentally thought it normal to get a phone call at one in the morning to come and pick a complete stranger up off the street. Those are the kind of friends we all need.)
Might I just finally add that I love that Sho is already lost, just from the sight of those amazing eyes that Jun has.