When considering adaptation measures and global climate mitigation goals, stakeholders need regional-scale climate projections, including the range of plausible warming rates. To assist these stakeholders, it is important to understand whether some locations may see disproportionately high or low warming from additional forcing above targets such as 2 K (ref. ). There is a need to narrow uncertainty in this nonlinear warming, which requires understanding how climate changes as forcings increase from medium to high levels. However, quantifying and understanding regional nonlinear processes is challenging. Here we show that regional-scale warming can be strongly superlinear to successive CO2 doublings, using five different climate models. Ensemble-mean warming is superlinear over most land locations. Further, the inter-model spread tends to be amplified at higher forcing levels, as nonlinearities grow--especially when considering changes per kelvin of global warming. Regional nonlinearities in surface warming arise from nonlinearities in global-mean radiative balance, the Atlantic meridional overturning circulation, surface snow/ice cover and evapotranspiration. For robust adaptation and mitigation advice, therefore, potentially avoidable climate change (the difference between business-as-usual and mitigation scenarios) and unavoidable climate change (change under strong mitigation scenarios) may need different analysis methods.