We demonstrate Co40Fe30Ni30 medium-entropy alloy is a suitable Co-rich ternary CoxFeyNiz (x >= y >= z) alloy precursor for designing high-entropy magnetic alloys having superior semi-hard magnetic properties. Mechanical alloying of the constituent metal powders 40 at.% Co, 30 at.% Fe, and 30 at.% Ni for 12 h resulted in a nanocrystalline Co40Fe30Ni30 alloy comprised of the gamma phase. The alloy exhibited semi-hard magnetic behavior at ambient temperature; the intrinsic coercivity (H-CI) and saturation magnetization (M-S) was similar to 4.35 kA/m and similar to 141 Am-2/kg, respectively. At sub-ambient temperatures, the alloy maintained semi-hard magnetic behavior; both H-CI and M-S increased by similar to 1.4 times and similar to 4%, respectively, from 300 K to 60 K. The estimated mu(H) (the maximum magnetic moment per atom) was similar to 1.51 mu(B). At elevated temperatures, up to T <= similar to 570 K, the as-prepared alloy powder maintained the gamma phase, and after that alpha phase precipitated out. Thermal-treatment increased M-S by similar to 13% and decreased H-CI by similar to 31%, yet the alloy retained semi-hard magnetic behavior. At cryogenic temperatures, the thermally-treated alloy powders exhibited magnetic behavior similar to that of as-prepared alloy powder, i.e., both H-CI and M-S increased with the decrease in T. Grey relational analysis proposed Co40Fe30Ni30 as a suitable medium-entropy alloy precursor for designing novel high-entropy magnetic alloys having superior semi-hard magnetic properties.