  Superconductivity and its underlying mechanisms are one of the most active research fields in condensed-matter physics. An important question is how to enhance the transition temperature $T_{\rm c}$ of a superconductor. In this respect, the possibly positive role of valence-skipping elements in the pairing mechanism has been attracting considerable interest. Here we follow this pathway and successfully enhance $T_{\rm c}$ up to almost 6 K in the simple chalcogenide SnTe known as topological crystalline insulator by doping the valence-skipping element In and codoping Se. A high-pressure synthesis method enabled us to form single-phase solid solutions Sn$_{1-x}$In$_{x}$Te$_{1-y}$Se$_{y}$ over a wide composition range while keeping the cubic structure necessary for the superconductivity. Our experimental results are supported by density-functional theory calculations which suggest that even higher $T_{\rm c}$ values would be possible if the required doping range were experimentally accessible. 
Tailoring band-structure and band-filling in a simple cubic (IV, III) -   VI superconductor