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In comparison with conventional semiconductors, most two-dimensional semiconductor (2DSC) materials are dissimilar in structure and composition. Herein, we use electron-counting rules to propose a large family of 2DSCs, which all adopt the same structure and are composed of solely main group elements. Advanced density functional theory calculations are used to predict a number of novel 2DSCs, and we show that they span a large range of lattice constants, band gaps, and band edge states. As a result, they are good candidate materials for heterojunctions. This family of two-dimensional materials may be instrumental in the fabrication of 2DSC devices that may rival the currently employed 3D semiconductors.