Raman spectroscopy is a key technique for the identification and structural interrogation of molecules. It generally exploits changes in vibrational state within individual molecules which produce, in the scattered light, frequencies that are absent in the incident light. Considered as a quantum optical process, each Raman scattering event involves the concurrent annihilation and creation of photons of two differing radiation modes, accompanying vibrational excitation or decay. For molecules of sufficiently high symmetry, certain transitions may be forbidden by the two-photon selection rules, such that corresponding frequency shifts may not appear in the scattered light. By further developing the theory on a formal basis detailed in other recent work [J. Chem. Phys. 144, 174304 (2016)], the present analysis now addresses cases in which expected selection rule limitations are removed as a result of the electronic interactions between neighboring molecules. In consequence, new vibrational lines may appear – even some odd parity (ungerade) vibrations may then participate in the Raman process. Subtle differences arise according to whether the input and output photon events occur at either the same or different molecules, mediated by intermolecular interactions. For closely neighboring molecules, within near-field displacement distances, it emerges that the radiant intensity of Raman scattering can have various inverse-power dependences on separation distance. A focus is given here to the newly permitted symmetries, and the results include an extended list of irreducible representations for each point group in which such behavior can arise.