Ah, the sad realities of cheap modern construction.

Yes there are things that can be done. This is a common question on the Home repair Reddit site. But they all are costly, and sometimes it takes several attempts to remedy the problem. If you owned the house, the best solution is to erect a 2x4 stud wall on the wall which is transmitting the neighbors noise. But the studs cannot touch the present wall. The cavity is then filled with dense blown in insulation, and instead of dry wall 3/4" MDF panels are applied to the studs, joints finished like dry wall and painted.