I could add that for the ministries you don't own, there's a special card that allows you to influence the SAPD into carrying out the policies you want to carry out at the price of 1-2 party resources.
Plus, if you have influenced the SAPD enough, you could integrate them back into the SPD.
how can I influence them
By paying party resources to the SAPD to carry out the policies you'd wish to carry out through a ministry you don't have.
In the actual game, however, this isn't implemented.