Graphene plasmonic structures with long-range layering periodicity are presented. Resonance energy scaling with the number of graphene layers involved in plasmonic excitation allows these structures to support multiple plasmonic modes that couple and hybridize due to their physical proximity. Hybridized states exhibit bandwidth enhancements of 100-200% compared to unhybridized modes, and resonance energies deviate from what is usually observed in coupled plasmonic systems. Origins of this behavior are discussed, and experimental observations are computationally modeled. This work is a precursor and template for the study of plasmonic hybridization in other two-dimensional material systems with layering periodicity.