We show that a nonlinear Hamiltonian evolution can transform an SU(3)
coherent state into a superposition of distinct SU(3) coherent states, with a
superposition of two SU(2) coherent states presented as a special case. A phase
space representation is depicted by projecting the multi-dimensional Q-symbol
for the state to a spherical subdomain of the coset space. We discuss
realizations of this nonlinear evolution in the contexts of nonlinear optics
and Bose--Einstein condensates