This paper extends Compositional Equivalence ---which is a structural correspondence type aimed for multiplex networks--- by incorporating actor attributes in the modelling of the network relational structure as diagonal matrices. As an illustration, we construct the positional system of the Florentine families' network in the 15th century with Business and Marriage ties together with relevant characteristics acquired from the actors such as families' financial Wealth and their number of Priorates. Different representations of the cumulated person hierarchies reveal that adding Wealth in the modelling provides a more accurate picture of what the substantial narrative says about this network.