  As a sequel to previous work, we extend the study of the ground state
configuration of the $D=3$, Wilson-Fisher conformal $O(4)$ model. In this work,
we prove that for generic ratios of two charge densities, $\rho_1/\rho_2$, the
ground-state configuration is inhomogeneous and that the inhomogeneity
expresses itself towards longer spatial periods. This is the direct extension
of the similar statements we previously made for $\rho_1/\rho_2\ll 1$. We also
compute, at fixed set of charges, $\rho_1,\, \rho_2$, the ground state energy
and the two-point function(s) associated with this inhomogeneous configuration
on the torus. The ground state energy was found to scale
$(\rho_1+\rho_2)^{3/2}$, as dictated by dimensional analysis and similarly to
the case of the $O(2)$ model.
  Unlike the case of the $O(2)$ model, the ground also strongly violates
cluster decomposition in the large-volume, fixed-density limit, with a
two-point function that is negative definite at antipodal points of the torus
at leading order at large charge.
