Many-body effects arise from the collective behaviour of large numbers of interacting particles, for example, electrons,
and the properties of such a system cannot be understood considering only single or non-interacting particles1–5. Despite
the generality of the many-body picture, there are only a few examples of experimentally observing such effects in molecular systems6–8. Measurements of the local density of states of single molecules by scanning tunnelling spectroscopy
is usually interpreted in terms of single-particle molecular orbitals9–11. Here, we show that the simple single-particle
picture fails qualitatively to account for the resonances in the tunnelling spectra of different charge states of cobalt
phthalocyanine molecules. Instead, these resonances can be understood as a series of many-body excitations of the different ground states of the molecule. Our theoretical approach opens an accessible route beyond the single-particle picture in quantifying many-body states in molecules.