In this article, we define a family of \(C^*\) -algebras that are generated by a finite set of unitaries and isometries satisfying certain twisted commutation relations and prove their K-stability. This family includes the \(C^*\) -algebra of doubly non-commuting isometries and free twist of isometries. Next, we consider the \(C^*\) -algebra generated by an n-tuple of -twisted isometries with respect to a fixed \(n\atopwithdelims ()2\) -tuple of commuting unitaries (see [14]). Identifying any point of the joint spectrum of the commutative \(C^{*}\) -algebra generated by \((\{U_{ij}:1\le i<j \le n\})\) with a skew-symmetric matrix, we show that the algebra is K-stable under the assumption that does not contain any degenerate, skew-symmetric matrix. Finally, we prove the same result for the \(C^*\) -algebra generated by a tuple of free -twisted isometries.
