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In an attempt to incorporate tin (Sn) into high-entropy alloys composed of refractory metals Hf, Nb, Ti and Zr with the addition of 3<i>d</i> transition metals Cu, Fe, and Ni, we synthesized a series of alloys in the system HfTiZrSn<i>M</i> (<i>M</i> = Cu, Fe, Nb, Ni). The alloys were characterized crystallographically, microstructurally, and compositionally, and their physical properties were determined, with the emphasis on superconductivity. All Sn-containing alloys are multi-phase mixtures of intermetallic compounds (in most cases four). A common feature of the alloys is a microstructure of large crystalline grains of a hexagonal (Hf, Ti, Zr)₅Sn₃ partially ordered phase embedded in a matrix that also contains many small inclusions. In the HfTiZrSnCu alloy, some Cu is also incorporated into the grains. Based on the electrical resistivity, specific heat, and magnetization measurements, a superconducting (SC) state was observed in the HfTiZr, HfTiZrSn, HfTiZrSnNi, and HfTiZrSnNb alloys. The HfTiZrSnFe alloy shows a partial SC transition, whereas the HfTiZrSnCu alloy is non-superconducting. All SC alloys are type II superconductors and belong to the Anderson class of “dirty” superconductors.