Can the current successes of global machine learning-based weather simulators be generalized beyond two-week forecasts to stable and accurate multiyear runs? The recently developed AI2 Climate Emulator (ACE) suggests this is feasible, based upon 10-year simulations with a network trained on output from a physics-based global atmosphere model using a grid spacing of approximately 110 km and forced by a repeating annual cycle of sea-surface temperature. Here we show that ACE, without modification, can be trained to emulate another major atmospheric model, EAMv2, run at a comparable grid spacing for at least ten years with similarly small climate biases -- a necessary prerequisite to wider applicability. With a comprehensive analysis from multiple temporal, spatial, and frequency domain perspectives, we show that ACE faithfully represents the spatiotemporal structure of EAMv2 precipitation and related variables. Finally, we show that a pretrained ACE network is able to adapt to a new global climate model simulation dataset with 10x fewer training steps than when starting from random initialization, all while still maintaining low levels of climate bias. Further analysis of these fine-tuning experiments reveal ACE's attractive ability to interpolate between distinct global climate models.