In my current company we use SAfE as a framework, and really push the Agile envelope with a lot of Teams doing work cooperatively and across Teams in our Trains (that have lots of Teams cooperating). The culture has been built up over time and we do well at cooperative planning and scheduling, keeping up the date on dependencies and workflows. All of it good on the Team side.
With a recent merger of the company one thing that was missing was integrating with the other Teams we interacted with at times. They loved the idea of our process and were happy to get on board, some did well as we integrated and Teams went out of the way to be accommodating. For others, not so much.
Teams can do Agile and when they put their minds to it, this works well.
Teams of Teams can also do it, as they cooperate and communicate. Being transparent on how dependencies are going there is a lot that can work well.
Even among different departments (Marketing, IT, etc) the process can work.
Though where it always needs that extra push is Upper Management.
Executives need to give more than lip service, it's easy to say "my whole Engineering Department is using Agile" but if they are waiting on equipment or resources from IT or HR (always need hires!) then things slow down. You can adjust but the culture needs to come from the top.
More than lip service Executives need to push the culture, speak the words and walk the walk. Be able to not just understand that the Teams working for them are doing cool stuff, but enable them from THE TOP so that Teams can continue doing cool things.
Companies make culture, and processes can enable that culture, but only so long as everyone is on board, otherwise its just Teams doing cool stuff.