An increasing number of scanning-probe-based spectroscopic techniques provides access to diverse electronic properties of single molecules. Typically, these experiments can only study a subset of all electronic transitions, which obscures the unambiguous assignment of measured quantities to specific quantum transitions. Here we develop a single-molecule spectroscopy that enables the access to many quantum transitions of different types, including radiative, non-radiative and redox, that is, charge-related, transitions. Our method relies on controlled alternating single-charge attachment and detachment. For read-out, the spin states are mapped to charge states, which we can detect by atomic force microscopy. We can determine the relative energies of ground and excited states of an individual molecule and can prepare the molecule in defined excited states. After a proof-of-principle demonstration of the technique on pentacene, we apply it to PTCDA, the scanning-probe luminescence of which has been interpreted controversially. The method may be used to guide, understand and engineer tip-induced chemical reactions as well as phosphorescence and fluorescence of individual molecules.