As someone else commented, a lot of times extra layers of drywall are added to add mass to a wall (this is a fairly effective solution). But there are complications to 'thickening' the wall like this (at least, if you want it to look professional in the end!).

There's a great document from the US HUD on the topic: https://www.hud.gov/sites/documents/DOC_16419.PDF

Heavy mass walls will keep all but the lowest noises from entering the room from outside, but it will also prevent the energy from your speakers or instruments from leaving the room, causing the room to ring at various modal frequencies.

You can absorb high-end and most mid-range frequencies using broadband absorbers on the wall and ceiling, but they're ineffective at capturing low-end. Treating the low end requires a different strategy.

The most effective solution for absorbing low-end in the room will be limp-mass membrane absorbers that are tuned to the lowest room modes. They'll be up to 18" thick, but they are by far the most efficient way to keep the low-end from ringing inside of your room.