seems that you have a bug, because it's normally the 2nd department that you get to control...
You have to have pass the several seminaries in HR dept and to have the Planning Dept under your control first
I was never able to take over the planning department in one game. But had Consulting, HR and Legal.
It's basically all about getting the KPIs to zero (ambition and pride) and finding all the triggers that make those numbers go down before the characters change states. If you put the world through a state change to soon then you don't get access to more triggers and the game is soft locked. I don't know if this is intentional because all selecta games are this flavor of broken.
For example you can end up passing the medical plan, talking to HR to have Planning committed, talking to Planning about it, replacing the pills, but she's 0 Ambition 30 Pride with zero events remaining and there's just physically no option to move forward. It's hard to tell if this is some poorly explained puzzle mechanic or bugs. Meanwhile some characters have events you can just repeat over and over to get them to zero.