  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.
