Quaternary-alloy MgxZn1−xO1−ySy thin films were grown quasi-epitaxially on c-plane sapphire substrates by pulsed laser deposition. Single-phase wurtzite MgxZn1−xO1−ySy films with compositions of 0.07 < x < 0.21 and y ≥ 0.8 were achieved using various ceramic targets. The S contents in the quaternary alloy films were far beyond the reported solid solubility limits of S in single-phase ternary alloy ZnO1−ySy films. The bandgap of MgxZn1−xO1−ySy, inferred from optical transmission measurements, was narrower than the bandgap of MgxZn1−xO while broadened compared with that of ZnO1−ySy. The broadening effect was enhanced with the increase of Mg content. The simultaneous substitution of cation (Zn2+) and anion (O2−) by isoelectronic elements (Mg2+ and S2−) offers further flexibility for the band-gap engineering and potentially facilitates the p-type doping of ZnO.