From my point of view, I would make sure the assigned teams have their own board for the project. Then, a product owner or anybody that would need to have a high-level view (planning for instance) could go onto Portfolio.
It really is a question of the perspective of the user and what level of information is relevant to them, at that time :)
To see this feature in action check out our recent dependencies demo here: https://www.youtube.com/watch?v=eQu5VsUqyZA Keeping on top of your dependencies is a key part of ensuring project success....
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