  We study a $SU(2)$-symmetric spin-${3}/{2}$ system on a bipartite lattice
close to the antiferromagnetic $SU(4)$-symmetric point, which can be described
by the $CP^{3}$ model with a perturbation breaking the symmetry from $SU(4)$
down to $SU(2)$ and favoring the N\'eel ordering. We show that the effective
theory of the perturbed model is not the usual $O(3)$ nonlinear sigma model
(NLSM), but rather the $O(3)\times O(2)$ NLSM. We show that in the presence of
perturbation, the topological charge $q$ of the $CP^{3}$ field is connected to
the $O(3)$-NLSM type topological charge of the spin texture $Q$ (defined in a
usual way via the unit N\'eel vector) by the relation $q=3Q$, thus under the
influence of the perturbation unit-charge skyrmions of $CP^{3}$ model bind into
triplets. We also show that in the general spin-$S$ case, symmetry breaking
from $SU(2S+1)$ to $SU(2)$ results in the general relation $2S
Q_{O(3)}=q_{CP^{2S}}$ between $CP^{2S}$ and $O(3)$ charges, so one can expect
$2S$-multiplet binding of skyrmions.
