We analyze the phase diagram associated with a pair of magnetic impurities trapped in a superconducting host. The natural interplay between Kondo screening, superconductivity, and exchange interactions leads to a rich array of competing phases, whose transitions are characterized by discontinuous changes of the total spin. Our analysis is based on a combination of numerical renormalization group techniques as well as semiclassical analytics. In addition to the expected screened and unscreened phases, we observe a new molecular doublet phase where the impurity spins are only partially screened by a single extended quasiparticle. Direct signatures of the various Shiba molecule states can be observed via radio-frequency spectroscopy.