We present the first experimental determination of the intra-atomic exchange energy between the inner 4f and the outer 6s5d shells in rare-earth elements. Inelastic electron tunneling spectroscopy on individual rare-earth atoms adsorbed on metal-supported graphene reveals an element-dependent excitation, with energy between 30 and 170 meV, linearly increasing with the spin angular momentum of the 4f shell. This observation is possible owing to the strong spin polarization of the outer shells, characteristic of rare-earth adatoms on graphene. This polarization gives rise to a giant magnetoresistance of up to 75% observed for Dy on graphene/Ir(111) single-atom magnets. Density functional theory calculations of the 6s5d shell spin polarizations and of their intra-atomic exchange constants with the 4f shell yield exchange energies in agreement with the experimental values. These results prove that the description of the spin dynamics in RE considering only the 4f - 5d interaction is oversimplified. A more realistic treatment requires us to consider a multishell intra-atomic exchange in which both 6s and 5d shells are taken into account, with the 4f - 6s contribution possibly prevailing over the 4f - 5d one. Our findings are important for the general understanding of magnetism in rare earths, whether they are in bulk compounds or as surface adsorbed atoms and clusters. The results presented here also push for a revision of the description of the spin dynamics in rare-earth-based systems.