MG,
First things first.. look for any penetrations including above any ceilings. Look for pipe, electrical, etc. These flanking paths can kill even the low 40's STC you should be getting. It sounds like you want to take a bit out of the full range sound coming from your space (including drums, guitars, etc). I would recommend that you do a couple of things. Yes, a second stud wall will give you a significant increase in performance over adding a single layer of 5/8"GB to the existing face. The airspace, is an integral part of the isolation system. If you can afford it, I would recommend that you build the new stud wall, say 2" away from the face of the existing wall. Then put as much as you can onto your side of the studs up to four layers of material... Do at least two layers of 5/8"GB, but combining dissimilar materials can help performance as well... like GG / PLywood / GB for example.
Make sure you seal EVERYTHING tight including floor joints, ceiling joints, edges of walls, electrical penetrations, etc with non-hardening silicon caulk. Overlap all the lamination layers and use construction adhesive along with proper length sheet rock screws to attach each layer.
Other possible 'improvements' include use of Resilient channel, but this requires a lot more attention to detail..
Use of (heavier) Quiet Rock for final layer
Use of Green Glue instead of construction adhesive..
It all comes down to cost vs performance..
FM