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Sulfur‐rich volcanic eruptions happen sporadically. If Stratospheric Aerosol Injection (SAI) were to be deployed, it is likely that explosive volcanic eruptions would happen during such a deployment. Here we use an ensemble of Earth System Model simulations to show how changing the injection strategy post‐eruption could be used to reduce the climate risks of a large volcanic eruption; the risks are also modified even without any change to the strategy. For a medium‐size eruption (10 Tg‐SO2) comparable to the SAI injection rate, the volcanic‐induced cooling would be reduced if it occurs under SAI, especially if artificial sulfur dioxide injections were immediately suspended. Alternatively, suspending injection only in the eruption hemisphere and continuing injection in the opposite would reduce shifts in precipitation in the tropical belt and thus mitigate eruption‐induced drought. Finally, we show that for eruptions much larger than the SAI deployment, changes in SAI strategy would have minimal effect. Plain Language Summary: The artificial injection of aerosols in the stratosphere (SAI) may help mitigate risks from increasing surface temperatures by reflecting some of the incoming sunlight. Such injections would need to be continued for decades, meaning that the chance is high for a sulfur‐rich volcanic eruption to happen during that time. When such an eruption happens, temperatures are reduced abruptly, and there might be changes in precipitation patterns if most of the aerosols are in only one hemisphere. We show that one could envision mitigation strategy during SAI that reduce the risks arising from the abrupt changes produced by volcanic eruption, by shifting where the artificial injections happen and their amount. However, this depends on the magnitude of the eruptions, as for those too large (5 times as big as the largest eruption of the 20th century) such mitigation strategies would simply not be enough. Key Points: It is likely that a large volcanic eruption would happen during an eventual Stratospheric Aerosol Injection (SAI) deploymentThe disruption to the stratospheric aerosol layer would require a modification of the SAI injection strategyWe show that the hydrological impacts of a large volcanic eruption could be mitigated by such a change in strategy [ABSTRACT FROM AUTHOR]