The isostructural alloying of two compounds with extremely different magnetic and thermo-structural properties has resulted in a new system, (MnNiSi)1-x(FeCoGe)x, that exhibits extraordinary magnetocaloric properties with an acute sensitivity to applied hydrostatic pressure (P). Application of hydrostatic pressure shifts the first-order phase transition to lower temperature ($Delta$ T=-41 K with P=3.43 kbar) but preserves the giant value of isothermal entropy change (-$Delta$S$max$=143.7 J/kg K for a field change of {Delta}B=5 T at atmospheric pressure). Together with the magnetic field, this pressure-induced temperature shift can be used to significantly increase the effective relative cooling power.
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