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 (∼2.4 kbar) lead to an extraordinary enhancement of the isothermal entropy change from -ΔS=44 to 89 J/kgK at ambient and 2.4 kbar applied pressures, respectively, for a field change of ΔB=5T, and is associated with a large relative volume change of about 7% with P=2.4 kbar.