The East Asian summer monsoon (EASM) is a dominant driver of East Asian climate, with variations in its strength potentially impacting the livelihoods of millions of people. Understanding, predicting and assessing uncertainties in these variations is therefore an important area of research. Here, we present a study of the projected 21st Century changes in the EASM using a ‘perturbed parameter ensemble’ (PPE) of HadGEM3-GC3.05 coupled climate models, which samples uncertainties arising from differences in model parameter values. We show that while the present-day performance of PPE members for leading order EASM metrics is comparable to CMIP5 models in many respects, the PPE also exposes model biases which exist for most, if not all, parameter combinations. These ‘structural’ model biases are found mainly in the low-level circulation over the South China Sea and west Pacific. We also show that future changes in regional circulation and precipitation are projected consistently across the PPE members. A more detailed moisture budget analysis of the precipitation changes in a region covering the Yangtze River valley shows that both dynamic and thermodynamic changes contribute to an increase in precipitation over the 21st century, but that the spread in this response across the PPE is mainly due to spread in the dynamic responses. We also discuss how the information provided by the PPE may be used in practice, considering the plausibility of the models, and giving examples of ways to sub-select ensemble members to capture the diversity in the moisture budget changes.