The hydrostatic pressure is expected to be an effective knob to tune the magnetostructural phase transitions of hexagonal MM'X alloys (M and M' denote transition metals and X represents main group elements). We perform magnetization measurements under hydrostatic pressure on an MM'X martensitic MnNi20.77Fe0.23Ge alloy. The magnetostructural transition temperature can be efficiently tuned to lower temperatures by applying moderate pressures, with a giant shift rate of -151 K/GPa. A temperature span of 30 K is obtained under the pressure, within which a large magnetic entropy change of -23 J⋅kg-1K-1 in a field change of 5 T is induced by the mechanical energy gain due to the large volume change. Meanwhile, a decoupling of structural and magnetic transitions is observed at low temperatures when the martensitic transition temperature is lower than the Curie temperature. These results show a multi-parameter tunable caloric effect that benefits the solid-state cooling.