I think it'd be interesting to allow ministers to rise up in positions. This way limited minister list for nations can be not so limited. You could have connected traits (E.g. corrupt kleptocrat is more likely to be a smiling oilman if head of government) and such for plausibility. Those in military parts of cabinet that suddenly rise to Head of State or Head of Government somehow would probably get military-related traits, etc.
Of course this would all have to be very rare, but it would also add a new element to rouge politicians. You could have people threatening to resign, etc. Maybe even have ministers change their ideology if you alienate them. Of course this can only happen if they have a 'moderate' ideology (Social Liberal, Market Liberal, Social Conservative) and anything more to the left/right of that would be very rare (Soc. Dem, Leninist, Fascist) or extraordinarily rare (Stalinist, National Socialist) as a random circumstance. IRL there were Fascists who became social conservatives or market liberals as Nazi Germany was falling, and especially Nazis who realized that it was all over and were forced to moderate their views or go into exile. Changing the ideology of the HoS or HoG would be astronomically rare and can only happen if the nation becomes too leftist, rightist, or moderate, forcing them to compromise.
If you wanted even more detail, people could have a chance to change their ideologies based on popularity of said ideology across the world if their own nation wasn't strong in upholding it. (E.g. Nazi Germany in its final days) This would also simulate the fall of Nazism as an ideology quite well.
Basically, I want a more dynamic minister system.