In QCD, the Eightfold Way organizes the number of baryons with respect to their flavor and color quantum numbers: for three light $(u,d,s)$ quark constituents, a spin-(1/2) baryon octet and a spin-(3/2) baryon decouplet emerge, because the antisymmetric baryonic wave function requires a symmetric spin-flavor part in the presence of the antisymmetric color wave function.
Alternatively, baryons can be modeled by topological objects called Skyrmions. Skyrmions arise if the third homotopy group satisfies $\pi_3(G/H)\neq 0$ in a symmetry breaking sequence $G\rightarrow H$: in QCD, the quark condensate spontaneously breaks the $SU(3)\times SU(3)\rightarrow SU(3)$ flavor symmetry yielding $\pi_3(SU(3))= Z$.
Now my first question is: since the existence of Skyrmions only requires spontaneous flavor symmetry breaking, can we infer the number of the different baryons in the Skyrmion model without any knowledge about color? In other words, could we infer from the symmetry breaking pattern itself (which yields $\pi_3(SU(3))= Z$) how many baryons exist in Nature?
And my second question is: could the number of baryons change for different flavor symmetry breaking patterns (which would not be allowed in QCD), such as $SU(3)\times SU(3)\rightarrow U(1)\times U(1)\times U(1)$ or $SU(3)\times SU(3)\rightarrow SU(2) \times SU(2)\times U(1)$?