  We prove a version of Temkin's local altered uniformization theorem. We show
that for any rig-smooth, quasi-compact and quasi-separated admissible formal
$\mathcal{O}_K$-model $\mathfrak{X}$, there is a finite extension $K'/K$ such
that $\mathfrak{X}_{\mathcal{O}_{K'}}$ locally admits a rig-\'etale morphism
$g\colon \mathfrak{X}' \to \mathfrak{X}_{\mathcal{O}_{K'}}$ and a
rig-isomorphism $h\colon \mathfrak{X}" \to \mathfrak{X}'$ with $\mathfrak{X}'$
being a successive semi-stable curve fibration over $\mathcal{O}_{K'}$ and
$\mathfrak{X}"$ being a poly-stable formal $\mathcal{O}_{K'}$-scheme. Moreover,
$\mathfrak{X}'$ admits an action of a finite group $G$ such that $g\colon
\mathfrak{X}' \to \mathfrak{X}_{\mathcal{O}_{K'}}$ is $G$-invariant, and the
adic generic fiber $\mathfrak{X}'_{K'}$ becomes a $G$-torsor over its
quasi-compact open image $U=g_{K'}(\mathfrak{X}'_{K'})$. Also, we study
properties of the quotient map $\mathfrak{X}'/G \to
\mathfrak{X}_{\mathcal{O}_{K'}}$ and show that it can be obtained as a
composition of open immersions and rig-isomorphisms.
