  In this article, we prove $K$-stability for a family of $C^*$-algebras, which
are generated by a finite set of unitaries and isometries satisfying twisted
commutation relations. This family includes the $C^*$-algebra of doubly
non-commuting isometries and free twist of isometries.
  Next, we consider the $C^*$-algebra $A_{\mathcal{V}}$ generated by an
$n$-tuple of $\mathcal{U}$-twisted isometries $\mathcal{V}$ with respect to a
fixed $n\choose 2$-tuple $\mathcal{U}=\{U_{ij}:1\leq i<j \leq n\}$ of commuting
unitaries (see \cite{NarJaySur-2022aa}). Under the assumption that the spectrum
of the commutative $C^*$-algebra generated by $(\{U_{ij}:1\leq i<j \leq n\})$
does not contain any element of finite order in the torus group
$\bbbt^{n\choose 2}$, we show that $A_{\mathcal{V}}$
  is $K$-stable. Finally, we prove the same result for the $C^*$-algebra
generated by a tuple of free $\mathcal{U}$-twisted isometries.
