  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 stack's 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 stack's interaction matrix. Finally, we predict
the absorption spectrum projected on the two orthogonal linear polarizations.
