A remarkable decrease of the structural transition temperature of MnNiSi from 1200 to < 300 K by chemically alloying it with MnFeGe results in a coupling of the magnetic and structural transitions, leading to a large magnetocaloric effect near room temperature. Application of relatively low hydrostatic pressures (similar to 2.4 kbar) lead to an extraordinary enhancement of the isothermal entropy change from -Delta S = 44 to 89 J/kgK at ambient and 2.4 kbar applied pressures, respectively, for a field change of Delta B = 5 T, and is associated with a large relative volume change of about 7% with P = 2.4 kbar.