1) Tear down your side of the wall. Build a second set of studs and then drywall over the second set. Insulate the wall of course.
2) Add as many layers with Green Glue in between as you can. There is no reason to stop at one layer. You can have all of the layers of 3/8 inch or thinner if you can find it with Green glue in between each layer that you want and still benefit. Just don't put more than 3 quarts per sheet in any layer. Adding two layers of 1/2 inch with two layers of Green glue will give you more benefit than 1 layer of 1 inch with one layer of Green glue. Of course at some point the cost benefit ratio will go down dramatically.
Remember only have one air cavity at most. Air cavities increase resonating frequency weak points in your sound protection.