In this paper, we introduce the class of (n,m)-metrically equivalent operators which is a generilazation of metrically
equivalent operators and n-metrically equivalent operators. We then look at some properties of this class and its relation
to some higher classes like quasi-isometries and the (n,m)-class (Q) operators. we also look at the relationship between
this class and other equivalence relations like metrically equivalent and n-metrically equivalent operators.