Remember one key to killing sound is air space. So a having an absorbent material, on top of a hard material, then air space, then another hard space. The sound wave is absorbed, then slows down going thru the hard material, the hits the air space and speeds up again, but runs into more absorbent material or another hard wall and bounces around in the air space till it decays.
I was lucky to be around one of the big name studios when they were building their second studio which would have a shared wall with first room. That is where I learned about air killing sound. They had a large space between rooms so after studio surface they had two layers of sheetrock. Then they built a framework in the space to hold rolls of insulation. What they did take regular wall insulation and roll it up in like a jelly roll, then stacked those floor to ceiling in the frame work. After that was a airspace about 18" wide. Then the same layer of insulation, double sheetrock, and studio wall to the other studio. It was very effective. I've seen variations on that used in other studios.
A friend owns a rehearsal studio and wasn't planning for totally killing sound between rooms, but to kill enough that bands wouldn't be bothered when playing. In general he built a frame work of 2x4's on edge out from the existing wall then sheetrock'd the wall. After that drilled large holes in the sheetrock and filled the walls with sand. Then tapping the walls down to get the sand to settle and keep adding more till solid. Then filled the holes and covered the walls with carpet. That wasn't too expensive and really deadens the sound.
Some combo of those idea could work for you.