In this paper we recover an [m,C]-isometric operators and (m, C)-isometric commuting tuples of operators on a Hilbert space studied respectively in [11] and [16], we introduce the class of [m,C]-isometries for tuple of commuting operators. This is a generalization of the class of [m,C]-isometric commuting operators on a Hilbert spaces. A commuting tuples of operators S = (S1, · · · ,Sp) ∈ B(H)p is said to be [m,C]-isometric p-tuple of commuting operators if Ψm ( S,C ) := m∑ j=0 (−1)m− j ( m j )(∑ |α|= j j! α! CSαCSα ) = 0 for some positive integer m and some conjugation C. We consider a multi-variable generalization of these single variable [m,C]-isometric operators and explore some of their basic properties.