The magnetostructural coupling between the structural and the magnetic transition plays a crucial role in magnetoresponsive effects in a martensitic-transition system. A combination of various magnetoresponsive effects based on this coupling may facilitate the multifunctional applications of a host material. Here, we demonstrate a possibility to obtain a stable magnetostructural coupling in a broad temperature window from 350 to 70 K, showing tunable magnetoresponsive effects, based on simultaneous manipulation of the phase stability and the magnetic structure by suitable chemical substitution of iron in MnNiGe. The resultant MnNiGe:Fe exhibits a magnetic-field-induced martensitic transition from paramagnetic austenite to ferromagnetic martensite, featuring (i) a large volume increase, (ii) a distinct magnetization change, (iii) small thermal hysteresis and (iv) a giant negative magnetocaloric effect. The results indicate that stable magnetostructural coupling is accessible in hexagonal phase-transition systems to attain the magnetoresponsive effects with broad tunability.