We present a combined scanning transmission electron microscopy-electron energy loss spectroscopy (STEM-EELS) investigation into the mode symmetries of plasmonic nanoparticle trimer and tetramer structures. We obtain nanometer-resolved energy loss spectra for both trimer and tetramer structures and compare these to boundary element method simulations. We show that EELS, in conjunction with eigenmode simulations, offers a complete characterization of the individual superstructures, and we trace the evolution of both optically dark and bright modes and identify multipolar mode contributions. We then apply this technique to tetramer structures that exhibit an expanded range of mode symmetries for two-dimensional and three-dimensional self-assembled geometries. These findings provide a comprehensive experimental account of the available photonic states in self-assembled nanoparticle clusters.