  For a compact Riemannian manifold $M^{n+1}$ acted isometrically on by a
compact Lie group $G$ with cohomogeneity ${\rm Cohom}(G)\geq 2$, we show the
Weyl asymptotic law for the $G$-equivariant volume spectrum. As an application,
we show in the $C^\infty_G$-generic sense with a certain dimension assumption
that the union of min-max minimal $G$-hypersurfaces (with free boundary) is
dense in $M$, whose boundaries' union is also dense in $\partial M$.
