Having been called in on many occasions to remedy situations as you describe - a common by-product of many new cross functional teams and most organizational systems that are somewhat 'silo'd' by function/expertise - the best solution is also the one that develops the team for high performance.
Facilitate the development of:
1- A collective Global view of the system (organization and wider environment) in which the team operates, so that everyone gets a sense they're part of the same world
2- A clear, rational value chain, understanding the value each team member/function brings to the table. This is also opportunity to achieve a critical step of 'differentiation', so that optimal integration can happen.
3- A collective view of the forces/dynamics/influences (organizational, systemic, cultural, individual perceptions) that impact the future success of the team, and what people want to do about mitigating barriers, supporting success
4- A sense of responsibility/accountability for the status quo per 'stakeholder' - and what they want to do about it going forward to engender team success
5- A collective vision - a clear picture of an ideal future scenario including team/individual goals, roles, process and relationships. (If there are bottlenecks in the value chain, this is where such issues can be solved by the group, honoring the skills and value each member brings to the team)
6- Common Ground (what people want to achieve together, solutions) and an Action Plan with clear deliverables, accountabilities - addressing both functional and relational contexts
Its a simple formula, but not necessarily easy to design/facilitate. There are a variety of dialogues/groups tasks to best serve the planning process above, best when customized for the group/players and culture. When a group goes through these steps together and engages in the inevitable 'take it to the mountain' dialogues this process engenders, leads to unprecedented team synergy/success.