Aryl isocyanates are introduced as comonomers for ring-opening copolymerization (ROCOP) with epoxides. Informed by studies of reaction kinetics, we show that divergent sequence selectivity for AB- and ABB-type copolymers can be achieved with a single dimagnesium catalyst. The resulting materials respectively constitute a new class of polyurethanes (PUs) and a new class of materials featuring an unprecedented backbone structure, the polyallophanates (PAs). The successful use of isocyanate comonomers in this way marks a new direction for the field of ROCOP while providing distinct opportunities for expansion of PU structural diversity. Specifically, the methodology reported herein delivers PUs featuring fully substituted (tertiary) carbamyl nitrogen atoms, a structural motif that is almost inaccessible via extant polymerization strategies. Thus, in one step from commercially available comonomers, our methodology expands the scope of ROCOP and gives access to diverse materials featuring both privileged (PU) and unexplored (PA) microstructures.