Assuming it's yours, or you know you'll be there a while, you can blow in the insulation like suggested. Punch small holes on top of each bay and blow the insulation in. I'm not sure if those machines can be rented or you might need a professional. Should'nt be too much for one wall.
THEN... there's insulation sheetrock you can cover the wall with after you blow the insulation in. They used to sell them at Hme Depot/ Lowes, not sure if they still do. The insulation sheetrock absorbs the sound well.
If.... you were building from scratch with rehab or new constructuion, you could build either two walls with a (small) space in between them or one wall on a 2x6 baseplate instead of the normal 2x4 plate. On this 2x6 plate you would alternate each verticle 2x4 from your wall to the neighbor's wall, so every other beam would be on your wll and vice versa. This will "seperate" the two walls from each other thus cancelling out a lot of noise. When there's seperation and an air space, the sound is not as obvious. This application is often use in dedicated Home Theater rooms where people don't want other rooms to hear the loud music/sounds.