When multiple Scrum Teams are working together on the same product, each team should not maintain a separate Product Backlog. According to the Scrum Guide, the Product Backlog is the single source of truth for the product, and it is owned and managed by the Product Owner 11. Having multiple Product Backlogs for the same product would create confusion, inconsistency, and duplication among the Scrum Teams and the stakeholders. It would also compromise the transparency, the alignment, and the value of the product development.
Instead of having separate Product Backlogs, the Scrum Teams should work from a common Product Backlog that reflects the vision, the goal, and the priorities of the product 22. The Product Owner should collaborate and communicate with the Scrum Teams and the stakeholders to ensure that the Product Backlog is clear, refined, and ordered. The Scrum Teams should coordinate and integrate their work to deliver a single Integrated Increment that meets the Definition of Done and the Product Goal every Sprint 33.