The discovery of building blocks offers new opportunities to develop and control properties of extended solids. Compounds with fluorite-type Bi2O2 blocks host various properties including lead-free ferroelectrics and photocatalysts. In this study, we show that triple-layered Bi2MO4 blocks (M = Bi, La, Y) in Bi2MO4Cl allow, unlike double-layered Bi2O2 blocks, to extensively control the conduction band.