A suite of chemistry‐climate model simulations, forced by pairs of anthropogenic forcings [comprising greenhouse gases (GHGs), ozone depleting substances (ODSs), or aerosols], were employed to investigate whether the high‐latitude Southern Hemisphere (SH) circulation response to these forcings is linearly additive, a common assumption in attribution studies. We find that the geographical pattern of sea‐level pressure (SLP) response to a combination of GHGs and ODSs is linearly additive. However, we find significant differences in the SLP response when combining GHGs and aerosols compared to the sum of the individual forcings, a non‐additivity that is currently masked by the dominance of the ODSs forcing. This non‐linearity also results in changes to the SH split jet. These results were obtained using a coupled chemistry‐climate model, indicating that the non‐linear response is due to chemical interactions between the forcing agents. As such, future simulations investigating a post‐ozone hole Southern Hemisphere climate should consider this chemical interaction.