Advances in molecular electronics depend on the ability to control the charge and spin of single molecules at the interface with a metal. Here we show that bonding of metal-organic complexes to a metallic substrate induces the formation of coupled metal-ligand spin states, increasing the spin degeneracy of the molecules and opening multiple spin relaxation channels. scanning tunnelling spectroscopy reveals the sign and magnitude of intramolecular exchange coupling as well as the orbital character of the spin-polarized molecular states. We observe coexisting Kondo, spin, and vibrational inelastic channels in a single molecule, which lead to pronounced intramolecular variations of the conductance and spin dynamics. The spin degeneracy of the molecules can be controlled by artificially fabricating molecular clusters of different size and shape. By comparing data for vibronic and spin-exchange excitations, we provide a positive test of the universal scaling properties of inelastic Kondo processes having different physical origin.