Anthropogenic aerosols over South and East Asia currently have a stronger impact on the Asian Summer Monsoon (ASM) than greenhouse gas emissions, yet projected aerosol emission changes in these regions are subject to considerable uncertainty in timescale, location, emission type, and even the sign of the change, implying large uncertainties in future ASM change. In addition, aerosol changes in either South or East Asia cause circulation anomalies that affect both countries and neighbouring regions. We use a circulation/climate model to demonstrate that the sum of ASM responses to individual aerosol emission reductions in each region is very different to the response to simultaneous reductions in both regions, implying the ASM response to aerosol emissions reductions is highly nonlinear. The phenomenon is independent of whether aerosols are scattering or absorbing, and is driven by large-scale teleconnections between the two regions. The nonlinearity represents a new source of uncertainty in projections of ASM changes over the next 30-40 years, and limits the utility of country-dependent aerosol trajectories when considering their Asia-wide effects. To understand likely changes in the ASM due to aerosol reductions, countries will need to accurately take account of emissions reductions from across the wider region, rather than approximating them using simple scenarios and emulators. The nonlinearity in the response to forcing therefore presents a regional public goods issue for countries affected by the ASM, as the costs and benefits of aerosol emissions reductions are not internalised; in fact, forcings from different countries work jointly to determine outcomes across the region.