  Let $(M^{n+1},g)$ be a closed Riemannian manifold, $n+1\geq 3$. We will prove
that for all $m \in \mathbb{N}$, there exists $c^{*}(m)>0$, which depends on
$g$, such that if $0<c<c^{*}(m)$, $(M,g)$ contains at least $m$ many closed
$c$-CMC hypersurfaces with optimal regularity. More quantitatively, there
exists a constant $\gamma_0$, depending on $g$, such that for all $c>0$, there
exist at least $\gamma_0c^{-\frac{1}{n+1}}$ many closed $c$-CMC hypersurfaces
(with optimal regularity) in $(M,g)$. This extends the theorem of Zhou and Zhu,
where they proved the existence of at least one closed $c$-CMC hypersurface in
$(M,g)$.
