In this work, we, for the first time, demonstrate a comprehensive model of the multi-level Spin-Orbit torque (SOT)-MRAM. Scalability, stochasticity, and variations of the multi-level SOT-MRAM are captured within a unified model framework based on the modified Preisach model of hysteresis. The model functionalities are verified by experimental data from four types of multi-level SOT devices fabricated by us and others, including the major switching loop, minor loops, device-size dependence, and the variation of intermediate states.