Just catching up with this and would like to add to points from my experience.
Fletch had terrible SA when I first rehomed him - he was 4 and started off as an only dog. Despite being a confident dog, he would howl when left and could keep up the howling for hours - it was, I suspect, the reason he was rehomed. I cured his SA when left very easily, but to honest, still can't go to the loo and shut the door without a howl if he notices!
Rehoming other dogs (I have 3 dogs) didn't have any negative or positive affect on his SA in general - he's still perfectly fine being left as they all are. However, he will howl for hours if I go out with Pip and leave him, even though Cindy is there; if I go out just with Cindy, no problems. This isn't really SA nor is it undying love for Pip as he's perfectly OK when he is the one being taken out
- it's just Fletch being Fletch! Pip is fine being left without Fletch.
However, I would really recommend that you waited until your dog has got over his teenage 'Kevin' stage before you considered another dog. All of mine have quickly picked up each others' bad habits (apart from Fletcher's howling!) and they are 6, 8/9 and 15 (I rehomed Pip at 6ish when Fletch was 4, and I've had Cindy, a yorkie, for 7 months). Even Cindy at 15 has picked up their bad habits!