What you describe kind of suggests upholding strict divisions per team like that is one of the main causes of the problem.
Wouldn't being more flexible of temporarily joining another team as a guest work? I imagine that for a number of situations this could work:
- I want to do x, my team needs it
- But we're responsible for X, and x falls under that
- When can you do it?
- We're understaffed, so years from now
- Fine I'll do it for you, I need it now
- Didn't you hear we are responsible for X? If x is not done right we are the ones who get in trouble for that.
- So make me a temporary guest member of your group, vet my work to make sure it's ok, and share the credit for x.
- Ok, that actually sounds like a good return on investment for us, welcome to the team!