Hi Robot8A, sorry if I reverted the values of network tag without notifying it to you, but please let’s not start an edit war.
I have been mapping bus lines in Marche for many years using network values like “Extraurbano Ancona” or “Urbano Jesi” because it seems to me the most appropriate way to describe how bus service is organised here.
Have a look at the company websites (https://startspa.it/ -> Servizi, https://www.conerobus.it/ -> Orari , https://www.adriabus.eu/orari/): intercity (extraurbano) and different city lines (urbano) are grouped in different pages, ticket and pass fares are different and so on, so in my opinion they fall in the definition of a network.
Start Plus is not a network, is a “società consortile”, as you have correctly entered in Wikidata, but “Start” is already tagged as operator; otherwise distinguish intercity and city bus lines is a valuable information to store, e.g. in Ascoli Piceno if you have a city pass from Start, you cannot use Start intercity buses, not even within the city.