Alpine mass movements can generate process cascades involving different materials including rock, ice, snow, and water. Numerical modelling is an essential tool for the quantification of natural hazards, but state-of-the-art operational models reach their limits when facing unprecedented or complex events. Here, we advance our predictive capabilities for process cascades on the basis of a three-dimensional numerical model, coupling fundamental conservation laws to finite strain elastoplasticity. Through its hybrid Eulerian-Lagrangian character, our approach naturally reproduces fractures and collisions, erosion/deposition phenomena, and multi-phase interactions, which finally grant very accurate simulations of complex dynamics. Four benchmark simulations demonstrate the physical detail of the model and its applicability to real-world full-scale events, including various materials and ranging through four orders of magnitude in volume. In the future, our model can support risk-management strategies through predictions of the impact of potentially catastrophic cascading mass movements at vulnerable sites.