We extend our theoretical description of optical excitations in binary plasmonic supercrystals made of two types of metal nanoparticles to three common cubic structures: sodium chloride (NaCl), zincblende (ZnS), and auricupride (Cu$_3$Au). Our microscopic model of plasmon polaritons in supercrystals incorporates dipole and quadrupole nanoparticle excitations, their interactions, and their coupling with photons. We calculate the plasmonic energy band dispersion in the first Brillouin zone of the supercrystal and demonstrate its dependence on the material properties of the nanoparticles and the symmetry properties of the structures. To gain further insight into the coupling of different excitations and develop a set of symmetry selection rules for each structure, we complement our calculations with an extensive group theory analysis. Comparing the results across various structures makes our symmetry analysis more general, enabling us to observe selection rules that apply to multiple structures.
