Future climate scenario projections are usually run with prescribed atmospheric CO<sub>2</sub> concentrations. However, by not allowing the carbon cycle to interactively respond to emissions in Earth System models, the role of carbon cycle feedbacks on contributions to differences in climate model projections may be undersampled. Here, we present the main findings of two Earth System Models (MPI-ESM1.2-LR and NorESM2-LM) run with CO<sub>2</sub> emissions to 2300 for three scenarios, two of which are climate overshoot scenarios, that were part of the Coupled Model Intercomparison Project Phase 6 (CMIP6). These experiments serve three important purposes: (i) an increasing focus on emissions driven runs, supplementing scenarios produced for the Coupled Climate-Carbon Cycle (C4MIP) and Carbon Dioxide Removal (CDRMIP) contributions to CMIP6; (ii) a focus on overshoot scenarios; and (iii) an extension of results beyond 2100, the timescales at which some of the most significant differences play out. Of the two models, NorESM2-LM shows more asymmetry in its response to the same global mean temperature levels before and after peak warming, particularly in terms of its regional pattern of warming and Atlantic Meridional Overturning Circulation (AMOC) response, with a substantially weakened AMOC persisting for decades after peak warming that takes more than a century to recover. In contrast, MPI-ESM1.2-LR shows reversibility with AMOC strength and regional warming more closely following surface temperature, but with some climate signals such as sea-level rise and ocean deoxygenation essentially irreversible. This diversity in model responses highlights the need for further research with a larger model ensemble that focuses on long-term emissions-driven model runs, particularly for overshoot scenarios, for CMIP7.