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.
It sounds like your sentiment is part of the same problem in Europe - I mean you said it yourself, you saw delays on these combo trains.
Luckily Europe has high speed rail which does not allow your friend's party wagon to disrupt the schedule. You might imagine a TGV or ICE picking it up, but I don't think it will ever happen.
That's entirely up to the company operating that ICE or TGV train. Not saying it's going to happen - many companies don't let other's wagons on their trains. But many do.
BTW so far my friend's train was never delayed by his own fault, not sure what problem you're talking about - there's no problem, his train had usually the lowest priority (it costs money to have higher priority) so he's the one waiting for "normal" trains.
When I said there are delays, I meant the "normal" trains primarily. But sure, as he increases operation it's going to happen to him too.
Improve schedule planning and Amtrak won't have problems too.
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.