Ternary or more complex hydrogen-rich hydrides are the main hope of reaching room-temperature superconductivity at high pressures. Their chemical space is vast and its exploration is challenging. Here we report the investigation of the La–Mg–H ternary system using the evolutionary algorithm USPEX at pressures in the range 150–300 GPa. Several ternary superconducting hydrides were found, including thermodynamically stable P6/mmm-LaMg3H28 with TC = 164 K at 200 GPa, P/2m-LaMgH8, C2/m-La2MgH12 and P2/m-La3MgH16. In addition, novel binary hydrides were predicted to be stable at various pressures, such as Cm–Mg6H11, P1–MgH26, Fmm2-MgH30, P1–MgH38 and R3̄m-LaH13. We also report several novel low-enthalpy metastable phases, both ternary and binary ones. Finally, we demonstrate important methods of exploring very large chemical spaces and show how they can improve crystal structure prediction.