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In this article, we prove $K$-stability for a family of $C^*$-algebras, whichare generated by a finite set of unitaries and isometries satisfying twistedcommutation relations. This family includes the $C^*$-algebra of doublynon-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 afixed $n\choose 2$-tuple $\mathcal{U}=\{U_{ij}:1\leq i<j \leq n\}$ of commutingunitaries (see \cite{NarJaySur-2022aa}). Under the assumption that the spectrumof 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 $C^*$-algebragenerated by a tuple of free $\mathcal{U}$-twisted isometries.

$K$-stability of $C^*$-algebras generated by isometries and unitaries with twisted commutation relations