Many useful principles of self-assembly have been elucidated through studies of systems where multiple components combine to create a single structure. More complex systems, where multiple product structures self-assemble in parallel from a shared set of precursors, are also of great interest, as biological systems exhibit this behavior. The greater complexity of such systems leads to an increased likelihood that discrete species will not be formed, however. Here we show how the kinetics of self-assembly govern the formation of multiple metal-organic architectures from a mixture of five building blocks, preventing the formation of a discrete structure of intermediate size. By varying ligand symmetry, denticity, and orientation, we explore how five distinct polyhedra-a tetrahedron, an octahedron, a cube, a cuboctahedron, and a triangular prism-assemble in concert around Co-II template ions. The underlying rules dictating the organization of assemblies into specific shapes are deciphered, explaining the formation of only three discrete entities when five could form in principle.