Controlled fabrication of devices for plasmonics on suspended graphene enables obtaining tunable localized surface plasmon resonances (LSPRs), reducing the red-shift of LSPRs, and creating hybrid 3D–2D systems promising for adjustable dipole–dipole coupling and plasmon-mediated catalysis. Here, we apply a low-cost fabrication methodology to produce patterned aluminum nanostructures (bowties and tetramers) on graphene monolayers via electron-beam lithography and trap platinum (Pt) nanoclusters (NCs) within their hotspots by thermal annealing. We reveal the LSPRs of aluminum plasmonics on graphene using electron energy-loss spectroscopy (EELS) and energy-filtered transmission electron microscopy (EFTEM) in a monochromated scanning transmission electron microscope (STEM). The LSPRs of these nanostructures are measured to be between visible and ultraviolet regions of the spectrum and are confirmed by electromagnetic simulations. The antibonding dipole and bonding dipole modes of both structures are tuned by controlling their gap size. The tetramers enable the simultaneous excitation of both antibonding and bonding dipole modes at the poles of nanoprisms, while bowties allow us to excite these modes separately either at the poles or within the hotspot. We further show that the hybrid nanocavity–NC systems are in the intermediate coupling regime providing an enhanced plasmon absorption in the Pt NCs via the energy transfer from the antibonding dipole mode to the Pt NCs. The dipole LSPR of Pt NCs also couples to the bonding-type breathing mode in bowties. Our findings suggest that these hybrid nanocavity–graphene systems are of high application potential for plasmon-mediated catalysis, surface-enhanced fluorescence, and quantum technologies.