Addition built onto neighbour's wall
So, your addition is built directly onto your neighbour's wall, meaning that if they took their wall down you'd have an open side to your addition.
While it is not permitted to build onto a neighbour's wall, even if that wall is right on the property line, it's unlikely that you would be forced to remove your addition if, in fact, it's been there for a number of years and was built by a previous owner. A lawyer will help you determine your exact level of risk on that one.
As far as building up on this addition, you can technically do so provided that you conform to all local building bylaws and have the correct permits, and, most importantly, you don't attach the new construction to the neighbour's building! Hire a builder/renovator with a good reputation to guide you through the process.