  Exploring continuous time crystals (CTCs) within the symmetric subspace of
spin systems has been a subject of intensive research in recent times. Thus
far, the stability of the time-crystal phase outside the symmetric subspace in
such spin systems has gone largely unexplored. Here, we investigate the effect
of including the asymmetric subspaces on the dynamics of CTCs in a driven
dissipative spin model. This results in multistability, and the dynamics
becomes dependent on the initial state. Remarkably, this multistability leads
to exotic synchronization regimes such as chimera states and cluster
synchronization in an ensemble of coupled identical CTCs.
