Wow. You used the word "duke" over 20 times.
Yes, this is my most confusing post so far, I doubt I would understand it if I were to read it

Congratulations to SpaceDoG for understanding it

I will try to exlain it another way.
There are 2 departments A and B. Each department has a manager AM, BM and positions A1, A2, A3, B1, B2, B3.
So player #4 (AM position) gave position A1 to player #78 and A2 to player #130. Now there is a change, someone else became AM and #4 became BM. But his friends (#78 and #130) possess positions A1 and A2 while he is in control of B department now (B1, B2 positions).
Oh and you could also just bump out the 2nd Duke appoint the new 2nd Duke and moving his people to the offices of the 2nd Duke bumping the old offices and then the new 1st Duke gets empty offices. As for the swapping that would be easy. Just move offices with each duke ;-)
Yes, that could work...