Optical control of polyatomic molecules promises new opportunities in precision metrology and fundamental chemistry, as well as quantum information and many-body science. Contemporary experimental and theoretical efforts have mostly focused on cycling photons via excitation of a single electron localized to an alkaline earth (group 2)-like metal center. In this paper, we consider pathways towards optical cycling in polyatomic molecules with multi-electron degrees of freedom, which arise from two or more cycling electrons localized to p-block post-transition metal and metalloid (group 13, 14, and 15) centers. We characterize the electronic structure and rovibrational branching of several prototypical candidates using ab initio quantum chemical methods. Despite increased internal complexity and challenging design parameters, we find several molecules possessing quasi-closed photon cycling schemes with highly diagonal, visible and near-infrared transitions. Furthermore, we identify new heuristics for engineering optically controllable and laser-coolable polyatomic molecules with multi-electron cycling centers. Our results help elucidate the interplay between hybridization, repulsion, and ionicity in optically active species and provide new directions for using polyatomic molecules with complex electronic structure as a resource for quantum science and measurement.