Unexpected nonlinear variation in the composition and optical band gap was observed in an alloyed open-framework metal chalcogenide composed of supertetrahedral clusters. A tentative hypothesis was proposed to explain how the title compound [In28Se54(H2O)4]·24H+-PR· nH2O (PR = piperidine) exhibits a limitation in the S-alloying level and a large variation in the optical band gap.