Temporal dissipative Kerr solitons in optical microresonators enable the generation of ultrashort pulses and low-noise frequency combs at microwave repetition rates. They have been demonstrated in a growing number of microresonator platforms, enabling chip-scale frequency combs, optical synthesis of low-noise microwaves and multichannel coherent communications. In all these applications, accessing and maintaining a single-soliton state is a key requirement—one that remains an outstanding challenge. Here, we study the dynamics of multiple-soliton states and report the discovery of a simple mechanism that deterministically switches the soliton state by reducing the number of solitons one by one. We demonstrate this control in Si3N4 and MgF2 resonators and, moreover, we observe a secondary peak to emerge in the response of the system to a pump modulation, an effect uniquely associated with the soliton regime. Exploiting this feature, we map the multi-stability diagram of a microresonator experimentally. Our measurements show the physical mechanism of the soliton switching and provide insight into soliton dynamics in microresonators. The technique provides a method to sequentially reduce, monitor and stabilize an arbitrary state with solitons, in particular allowing for feedback stabilization of single-soliton states, which is necessary for practical applications.