Sure I can. On the same track you have many different companies operating their own lines, combined multi-operatoe lines, as well as irregular connections (again single and multiple operators combined).

I've seen multiple operators (some of them entirely private, some entirely state-owned corporations, some combinations) combine their trains on an EuroCity-labelled line more than a few times.

I have a friend who is working on founding his own train company and he's actually providing services to the state-owned corporations where they have him operate their wagons in his combined train, with his own locomotive. He operated a major intercity line several times this way (they use his service when there's a problem on the regular route) - and it stopped to recombine several times. I've personally been on a train ride that combined his private for-fun party wagon with an EC train.