During the late 20th and early 21st centuries the frequency of extreme precipitation increased markedly over the central United States despite only a modest increase in mean annual precipitation. Extreme precipitation in this agriculturally important region has local and global impacts such as reduced agricultural yields affecting international markets, increased runoff of nutrients that compromises water quality, and dramatic increases in soil erosion. Although climate projections indicate that extreme precipitation will increase further in coming decades, the robustness of this result to the specific model used and to changes in model resolution has not been fully explored. Here we use a systematic matrix of dynamically downscaled climate projections in a three-dimensional parameter space (regional climate model, global climate model, and resolution) to evaluate the robustness of projected increases in extreme precipitation over the central U.S. in light of model performance for the current climate. The matrix includes two regional climate models (RCMs; WRF-ARW and RegCM4), each driven by three global models (GCMs; HadGEM2-ES, MPI-ESM-LR, and GFDL-ESM2M), with each combination of regional and global model run using three grid spacings (50 km, 25 km, and 12 km). Results show complex interactions among the RCM, driving GCM, and resolution. As an example, RegCM4 is more sensitive to the choice of GCM than is WRF, with this sensitivity in turn varying with resolution. We also found some unexpected results such as a tendency for the frequency of heavy precipitation to decrease with finer grid spacing in RegCM4. Nevertheless, the trend in precipitation extremes is robust: warm-season extreme precipitation over the central U.S. becomes more common in future climates for every model configuration tested.