Dear Totera,
I added the consortial entity as the network, copying how they do it in Germany or Austria, where I have lived previous to Italy. Truth be said, usually passes are valid there regardless of the urban/suburban network of the line, unlike here.
However, I still think that the society should be cited as a network, as they are in charge of a common branding of buses and stops. As said in Contram Mobilità website: "Società di gestione del servizio di Trasporto Pubblico Locale extraurbano ed urbano per il bacino di Macerata."
The subnetwork could be mapped as network:metro (see https://www.openstreetmap.org/relation/15866528 as an example, and https://www.openstreetmap.org/relation/8192939 as an example of where I got the inspiration from).
Best,
Héctor