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Polar dielectric nanoresonators can support hybrid photon-phonon modes termed surface phonon polaritons with lengthscales below the diffraction limit. In the deep sub-wavelength regime the optical response of these systems was recently shown to diverge from that predicted through a standard dielectric description. Recently we developed an analytical, dielectric approach and applied it to spheres and planar heterostructures, reproducing anomalous features observed in experiment and microscopic calculations. In this Letter we develop tools to describe the nonlocal response of polar nanoresonators of arbitrary symmetry. Their validity is verified by comparison to our previous analytical work, before application to new systems. We show that nonlocal energy transfer into matter-like modes in the dielectric diminish field enhancement in nanoscale dimers and that strong nonlocal frequency shifts are possible in macroscopic systems comprised of nanoscopic layers.