Magmatic systems in the Earth’s mantle and crust contain multiple phases, including solid crystals, liquid melt and low viscosity fluids, at different proportions. However, the theories underpinning most physical models of magmatic systems describe magma as a single-phase fluid, or as two-phase solid-dominated or liquid-dominated mixtures. Connections among these flow regimes are poorly established, hindering our understanding of magma mushes at intermediate phase fractions, which is the perceived state of large crustal magma bodies. To address this knowledge gap, this project establishes a numerical model to study the mechanics of any multi-phase magma mixture. On a fundamental level, this model transcends the theoretical limitations of existing models and expands the range of possible volcanological investigations. On a broader level, unravelling the processes in magma bodies is critical for assessing the hazard they pose to society, particularly at supervolcanoes whose eruptive impacts extend globally.