In the unidimensional setting, the well known Pigou-Dalton transfer principle is the basic axiom to order distribution in terms of inequality. This axiom has a number of generalizations to the multidimensional approach which have been used to derive inequality measures. However, up to now, none of them has assumed the Pigou-Dalton bundle dominance criterion, introduced by Fleurbaey and Trannoy (2003). This principle captures the basic idea of the original Pigou-Dalton transfer principle, demanding that also in the multidimensional context "a transfer from a richer person to a poorer one decreases inequality". Assuming this criterion the aim of this paper is to characterize multidimensional inequality measures. For doing so, firstly we derive the canonical forms of multidimensional relative aggregative inequality measures which fulfil this property. Then we identify sub-families from a normative approach. The inequality measures we derive share their functional forms with other parameter families already characterized in the literature, the major difference being the restrictions upon the parameters. Nevertheless, we show that it is not necessary to give up any of the usual requirements to assume the Pigou-Dalton bundle criterion. Thus, in empirical applications it makes sense to choose measures that also fulfil this principle.