We investigated the effects of the addition of Co and carbon on the deformation behavior of new medium-entropy alloys (MEAs) designed by increasing the entropy of the conventional NiCrFe-type Alloy 600. The strength/ductility combination of carbon-free (NiCo)75Cr17Fe8 MEA was found to be 729 MPa/81% at 298 K and it increased to a remarkable 1212 MPa/106% at 77 K. The excellent strength and ductility of (NiCo)75Cr17Fe8 at cryogenic temperature is attributed to the increased strain hardening rate caused by the interaction between dislocation slip and deformation twins. Strength/ductility combinations of carbon-doped (NiCo)75Cr17Fe8C0.34 and (NiCo)75Cr17Fe8C0.83 at cryogenic temperature were observed to be 1321 MPa/96% and 1398 MPa/66%, respectively, both of which are superior to those of other high-entropy alloys (HEAs). Strength/ductility combinations of (NiCo)75Cr17Fe8C0.34 and (NiCo)75Cr17Fe8C0.83 at room temperature were found to be 831 MPa/72% and 942 MPa/55%, respectively and both are far superior to 676 MPa/41% of the commercial Alloy 600. Yield strengths of carbon-free and carbon-doped alloys comprised strengthening components from the friction stress, grain size strengthening, carbide strengthening and interstitial strengthening and excellent agreement between the predictions and the experiments was obtained. A design strategy to develop new MEAs by increasing the entropy of the conventional alloys was found to be effective in enhancing the mechanical performance.