It would depend on how the shared wall is built. At a minimum, you'll want to remove the drywall from your side prior to doing clips, channel, and double drywall or you'll have a triple leaf. If you're going to go to that effort, you might as well just put up another separate wall on your side (after removing drywall) and double drywall it.
This will be more effective for less money as it's completely decoupled (not the floor connection obviously) and you don't have to do clips/channel. The deeper space between will also lower the resonant frequency of the wall as does the double drywall.
Lastly, if you're going to do this, make the stud spacing different on your wall than on the neighbor's wall so they both have different resonances that can't complement each other.
In any case, make sure all outlets and other penetrations are boxed around and sealed and that the entire space is insulated fully.
Bryan