Inspired by recent advances in atomic homo and heterostructures, we consider the vertical stacking of plasmonic lattices as a new degree of freedom to create a coupled system showing a modified optical response concerning the monolayer. The precise design of the stacking and the geometrical parameters of two honeycomb plasmonic lattices tailors the interaction among their metallic nanoparticles. Based on the similarity of the lattice symmetry, analogies can be drawn with stacked atomic crystals, such as graphene. We use the multipolar spectral representation to study the plasmonic vertical stacks optical response in the near-field regime, emphasizing symmetry properties. The strong coupling of certain optical bands shows up as anticrossings in the dispersion diagram, resulting in the polarization exchange of the interacting bands. By leveraging these effects, we engineer the near-field intensity distribution. Additionally, lifting band degeneracy at specific points of the Brillouin zone is obtained with the consequent opening of minigaps. These effects are understood by quantifying the multipolar coupling among nanospheres belonging to the same and different sublattices, as well as the interlayer and intralayer nanoparticle interactions. Differences with the atomic case are also analyzed and explained in terms of the stacks interaction matrix. Finally, we predict the absorption spectrum projected on the two orthogonal linear polarizations.
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