Single-phase Mn50Ni40In10-xCux (x = 0, 1, 2, 4, 6, 8, and 10) Heusler alloys were synthesized by melt-spinning method. Martensitic transformation is retained within the whole composition range studied. The substitution of Cu for In leads to a drastic increase in the martensitic transformation temperature T-M from below room temperature to above 750 K, and enhances the antiferromagnetic character of the martensite. The increase in T-M is related to the increasing electron concentration e/a and decreasing cell volume V with Cu doping. The energy difference between martensite and austenite also increases with Cu doping, which tends to elevate the T-M. Cu doping can enhance the metallic bonding character in NiMn-based magnetic shape memory alloys (MSMAs) and is a grain refining strategy of their ribbons. The oriented columnar grains in In-rich samples change to fine equiaxial grains in Cu-rich samples. All this has a positive effect on the strength and ductility. The tensile strength of the Mn50Ni40Cu10 ribbon is 3.6 times higher than that of Mn50Ni40In6Cu4. So, Mn-Ni-Cu can be a promising all-d-metal Heusler alloy platform for developing MSMAs with interesting properties.