Dissipative Kerr solitons (DKS) are localized structures in optical resonators that arise from a double balance between dispersion and Kerr effect, and linear loss and parametric gain . The periodic nature of DKS corresponds to frequency combs. DKS can be generated in high-Q microresonators for diverse applications, from coherent communications to precision frequency synthesis . Most studies of DKS have focused on microresonator cavities operating in the anomalous dispersion regime, where the waveforms correspond to bright soliton pulses. Coherent microresonator combs can also be formed in the normal dispersion regime . The time-domain waveform corresponds to a localized dark-pulse structure, interpreted as two interlocked switching waves connecting the two branches of the bi-stability curve in continuous-wave-pumped Kerr resonators [2,3]. Each switching wave connects the two branches following an oscillating behavior. These type of Kerr combs are relevant for practical applications because they display unusually high power-conversion efficiency [4,5], but their physical dynamics remain largely unexplored. Here, we report the discovery of deterministic switching of dark pulse Kerr combs, where the number of oscillations that appear between the switching waves can be either increased or decreased one at a time. The switching dynamics observed here have intriguing similarities to the switching behavior of bright temporal solitons in anomalous dispersion microresonators , and they indicate that dark pulse Kerr combs arise as a complex interplay of dark solitons circulating in the cavity.