We report the effect of high hydrostatic pressure (up to 1.1 GPa) on magnetization and critical temperatures of the magnetic and magneto-structural transitions in the off-stoichiometric In-doped (Ni,Co)2Mn(Ga,In) alloys. The magnetization MM(5 K) of their martensitic phase significantly decreases under pressure and the value of dlnMM(5 K)/dP = −55 × 10−3 GPa−1 was observed in the Ni41Co9Mn33Ga14In3 alloy. The temperature of structural transition of the alloys from martensite to austenite, TM-A, shows a strong dependence on both pressure (dTM-A/dP = 60 K/GPa) and magnetic field. The complex mutual dependence of TM-A to both pressure and magnetic field produces a remarkable reduction of the transformation hysteresis.