As others have pointed out this is both a complex and unfortunately expensive task. Traditional sound proofing routes such as room in room will not work given lack of space so the likely best option is a complete rebuild using a system such as the ASC iso damp method. My former room in Portland (see my system description) was built to this method as was Robert Harleys as described in AS earlier this year. Most contractors however can not cope with the complexity of this type of work. Look for a contractor that is experience in passive house (ie extreme energy efficiency) building techniques as these are the closest approach.
Having done all you can the limitation will likely be the doors, this was something I was actually never able to solve despite a pair of acoustic doors into the room!
Having done all you can the limitation will likely be the doors, this was something I was actually never able to solve despite a pair of acoustic doors into the room!