High Mountain Asia (HMA) holds the highest concentration of frozen water outside the polar regions, serving as a crucial water source for more than 1.9 billion people. Precipitation represents the largest source of uncertainty for future hydrological modelling in this area. In this study, we propose a probabilistic machine learning framework to combine monthly precipitation from 13 regional climate models developed under the Coordinated Regional Downscaling Experiment (CORDEX) over HMA via a mixture of experts (MoE). This approach accounts for seasonal and spatial biases within the models, enabling the prediction of more faithful precipitation distributions. The MoE is trained and validated against gridded historical precipitation data, yielding 32% improvement over an equally-weighted average and 254% improvement over choosing any single ensemble member. This approach is then used to generate precipitation projections for the near future (2036-2065) and far future (2066-2095) under RCP4.5 and RCP8.5 scenarios. Compared to previous estimates, the MoE projects wetter summers but drier winters over the western Himalayas and Karakoram and wetter winters over the Tibetan Plateau, Hengduan Shan, and South East Tibet.