Single phase Mn_0.66Fe_1.29P_1-xSi_x (0 ≤ x ≤ 0.42) compounds were synthesized using the melt-spinning (rapid solidification) technique. All the compounds form in the Fe₂P-type hexagonal structure, except a Co₂P-type orthorhombic structure of the Si-free Mn_0.66Fe_1.29P compound. The compounds with 0.24 ≤ x ≤ 0.42 present a FM-PM phase transition, while the compounds with lower Si content show an AFM-PM phase transition. In the Mn_0.66Fe_1.29P_1-xSi_x compounds, T_C and ΔT_hys are not only Si content dependent, but also magnetic field dependent. By increasing the Si content from x = 0.24 to 0.42, T_C increases from 195 to 451 K and ΔT_hys is strongly reduced from ∼61 to ∼1 K. T_C increases and ΔT_hys decreases with increasing magnetic field, ΔT_C/ΔB is about 4.4 K/T. Mn_0.66Fe_1.29P_1-xSi_x compounds show large saturation magnetic moments with values up to 4.57 μ_B/f.u. A large MCE with a small thermal hysteresis is obtained simultaneously in Fe-rich Mn_0.66Fe_1.29P_1-xSi_x melt-spun ribbons.