Recent trends in CO₂ emissions and pledged emission reductions suggest that achieving the Paris Agreement without an ‘overshoot’ represents a great challenge. In such a pathway, substantial net-negative emissions via Carbon Dioxide Removal (CDR) are required, to reduce atmospheric CO₂ and bring global mean temperatures back to the target. While the feasibility of globally net-negative emissions is under intense discussion, Stratospheric Aerosol Injection (SAI) has been proposed as a feasible approach to temporarily offset anthropogenically-induced global warming, often framed as a temporary measure to both avoid exceedance of climatic tipping points and to reduce climate impacts on humanity. The complexities of the coupled response of the Earth system to CDR and SAI remain under-explored. Here, we apply a fully-interactive Earth system model to perform idealized temperature overshoot simulations, with prescribed emissions pathways and SAI deployment in three different regions: the tropics, Northern Hemisphere mid-latitudes, and Southern Hemisphere mid-latitudes. All SAI deployments limit mean global warming to below two degrees, though the tropical SAI deployment yields the strongest global cooling effect due to longer aerosol lifetime and enhanced radiative effectiveness. The climatic consequences of SAI depend strongly on deployment location, primarily via the evolution of the Atlantic Meridional Overturning Circulation (AMOC). While all experiments exhibit an initial CO₂-driven AMOC weakening, Northern Hemisphere SAI most effectively mitigates this decline by reducing northern high-latitude warming and preserving North Atlantic deep-water formation. Southern Hemisphere SAI induces the least influence on Northern Hemisphere high-latitude warming and therefore does not substantially mitigate the AMOC decline. These contrasting AMOC responses propagate throughout the Earth system, influencing Northern Hemisphere surface temperature, sea-ice evolution, tropical precipitation patterns, ocean ventilation, carbon uptake, and regional ocean acidification. Although many aspects of the surface climate converge after SAI termination, substantial legacy effects persist in slow components of the climate system for centuries, such as sea-level rise and permafrost. Our results demonstrate that SAI deployment strategies should not be evaluated solely by their ability to regulate global temperature; furthermore, the geographical distribution of SAI strongly influences regional climate trajectories and the long-term legacy of this intervention.