Multistability in Kerr resonators which are driven by continuous or modulated optical waves gives rise to the superposition of distinct nonlinear states, yielding a unique platform for studying complex soliton dynamics. Here, by pumping a crystalline microresonator with two lasers that are frequency detuned from each other by one or multiple cavity free spectral ranges, we go beyond the traditional bichromatic pumping framework and enter an unexplored multistability regime that allows observing novel dynamics including composite solitons and successive soliton collisions. We generate complex frequency comb patterns, observing the velocity mismatch between the solitons and the dual-pumping-induced lattice traps and showing the synchronization of the repetition rates of constituent distinct solitons under the influence of index-barrier-induced intersoliton repulsion. We also demonstrate soliton collisions and observe transient soliton response with spectral analysis and ultrafast imaging, highlighting the eigenfrequency of dissipative soliton dynamics that coincides the "soliton (S) resonance." Furthermore, we exploit the higher-order dispersion effect to manipulate the intrinsic group velocity mismatch between distinct solitons and demonstrate reversible switching between the composite soliton state and the soliton collisional state. Our findings bring to light the rich physics of the Kerr multistability and may equally be useful in microcomb-based spectroscopy and metrology.