Please take the time to read these frameworks which all purport to be tested successful frameworks for managing multiple teams in an agile way.
- Agility Path by the crew at Scrum.org and Ken Schwaber
- Disciplined Agile Delivery by Scott Ambler
- LeSS (Large Scale Scrum) by Larman and Vodde
- SAFe (Scaled Agile Framework) by
Before adopting any one consider how change works and reflect on whether you want to go whole hog, and have an organisational revolution, or whether you want to take smaller steps and adapt change in an incremental and focused way. For that you could consider David Anderson's Kanban Method, or Martin Kearns and Andrea Tomasini's Agile Transitions booklet.
Thanks to John Ogden for pointing me to Peter Stevens blog which has a good post on the topic.