Several years ago I worked for Citect on its shrink wrapped product (also called Citect). The company had several software development teams working on Citect and thinking back on it I saw the teams as separate, each team was independent and had a clear team identity, even though we all worked on the one product. It demonstrates that 'team' is not necessarily tied to 'product' but to 'project', and a product can have multiple projects. In fact, I now think that the concept of a team is inherently linked to an individual project. One team, one project.
It seems that having multiple teams on the one project is a conundrum. If the teams lack identity they become one large team. The advantage of a team is lost. A shared project a team inhibitor.
I feel that what the project manager sees as a single project must be broken down into separate projects that each team can own. A team needs something to own, it needs boundaries so it can celebrate success. The issue of collaboration between teams is another matter for the the "team of teams" team.
Agile developers will collaborate. Other will always find a way ...