Large thermal hysteresis in the (Mn,Fe)2(P,Si) system hinders an efficient heat exchange and thus limits the magnetocaloric applications. Substitution of manganese by vanadium in the Mn1-x1Vx1Fe0.95P0.593Si0.33B0.077 and Mn1-x2Vx2Fe0.95P0.563Si0.36B0.077 compounds enable a significant reduction in the thermal hysteresis without losing the giant magnetocaloric effect. For the composition closest to the critical one, where first-order crossovers to second-order phase transition in the series of x2 = 0.02, Mn0.98V0.02Fe0.95P0.563Si0.36B0.077 exhibits a thermal hysteresis that is reduced from 1.5 to 0.5 K by 67%, yielding an adiabatic temperature change of 2.3 K and magnetic entropy change of 5.6 J/kgK for an applied field of 1 T, which demonstrates its potential for highly efficient magnetic heat pumps utilizing low-cost permanent magnets.