In this paper, we introduce new concepts of (m, q)-isometries and (m, ∞)-isometries tuples of commutative mappings on metrics spaces. We discuss the most interesting results concerning this class of mappings obtained form the idea of generalizing the (m, q)-isometries and (m, ∞)-isometries for single mappings. In particular, we prove that if T = (T 1 , · · · , T n) is an (m, q)-isometric commutative and power bounded tuple, then T is a (1, q)-isometric tuple. Moreover, we show that if T = (T 1 , · · · , T d) is an (m, ∞)-isometric commutative tuple of mappings on a metric space (E, d), then there exists a metric d ∞ on E such that T is a (1, ∞)-isometric tuple on (E, d ∞).