We discuss models of interacting magnetic impurities coupled to a metallic host, which show one or more boundary quantum phase transitions where the ground-state spin changes as a function of the interimpurity couplings. The simplest example is realized by two spin-1/2 Kondo impurities coupled to a single orbital of the host. We investigate the phase diagram and crossover behavior of this model and present numerical renormalization-group results together with general arguments showing that the singlet-doublet quantum phase transition is either of first order or of the Kosterlitz-Thouless type, depending on the symmetry of the Kondo couplings. Thus we find an exponentially small energy scale within the Kondo regime, and a two-stage Kondo effect, in a single-channel situation. Connections to other models and possible applications are discussed.