In this study, we aimed to design and investigate a non-equiatomic high strength and ductile high entropy alloy (HEA) by controlling the FCC phase stability. A new Co-rich Co50Cr20Ni20Fe5Mn5 HEA was synthesized by vacuum arc remelting and processed through homogenization, cold rolling, and recrystallization. The alloy’s phase composition, mechanical properties, and plastic deformation behavior were characterized using X-ray diffraction (XRD), tensile testing, and Transmission Electron Microscopy (TEM) analysis. The tensile properties of the alloy were compared with those of the conventional Co20Cr20Ni20Fe20Mn20 HEA produced and processed using the same technique and route. The results showed that reducing the Fe and Mn concentrations while increasing the Co concentration reduced the FCC phase’s stability, leading to the occurrence of partial FCC to HCP phase transformation upon cooling from high temperature and TWIP-TRIP effects during tensile deformation. The Co50Cr20Ni20Fe5Mn5 HEA exhibited improved mechanical properties, including higher yield strength (502 MPa), ultimate tensile strength (1002 MPa), and total elongation (50%) compared to the reference Cantor HEA (405 MPa, 766 MPa, and 40%, respectively). The principal strengthening mechanisms contributing to the increased yield strength with higher Co concentration were identified as initial HCP phase strengthening and grain boundary strengthening. The enhancement in ultimate tensile strength and ductility is attributed to the TWIP-TRIP effects during the tensile deformation of the Co50Cr20Ni20Fe5Mn5 HEA.