  Kerr-induced synchronization (KIS) provides a new key tool for the control
and stabilization of the repetition rate of a cavity soliton frequency comb. It
enables direct external control of a given comb tooth of a dissipative Kerr
soliton (DKS) thanks to its capture by an injected reference laser. Efficient
KIS requires its coupling energy to be sufficiently large, and hence both the
comb tooth and intracavity reference power must be optimized, which can be
achieved through higher-order dispersion that enables phase-matched dispersive
waves (DWs), where comb teeth are on resonance. However, such a design is
highly restrictive, preventing arbitrary use of reference wavelengths away from
the DW(s). In particular, for large spectral separations from the main pump the
cavity dispersion yields large detuning between comb teeth and their respective
cavity resonances, thereby decreasing the coupling energy and rendering KIS to
be highly inefficient or practically impossible. Here, we demonstrate an
alternative KIS method where efficient synchronization can be tailored at
arbitrary modes as needed. Using a multi-color DKS created from multi-pumping a
microresonator, a synthetic DW at the second-color wavepacket can be
selectively created where otherwise dispersion is far too large for KIS to be
experimentally feasible. Since a unique group velocity for both colors exists
thanks to cross-phase modulation, the repetition rate disciplining of the
secondary color wavepacket through its KIS automatically translates into the
DKS microcomb control. We first investigate this color-KIS phenomenon
theoretically, and then experimentally demonstrate its control and tuning of
the soliton microcomb repetition rate. As a consequence, we demonstrate optical
frequency division that is uncoupled from the main pump that generates the DKS.
