I think it would be great if in the game your spouse(s)/lover(s) and your friend(s) would be more than just pawns to be used and gain more stats.
For example, if you have a friend or a lover they could try and ask for a title or a court position for themselves or their family/friends even lover. Or your spouses could try to make their family members/friends/lovers prosper more and gain a better contract if they are vassals.
Maybe your spouses could try to be involved in your realm like eunuchs can in Byzantium.
One thing I would really appreciate would be a spouse fighting for their child to be on the throne with more than a rare event limited to rulers with multiple spouses at the same time. A second marriage and a new birth should still feel important as it was historically. To that effect, the new step-mother could try to redraw the map to get her child a better lot at the expense of other heirs like what happened with Charles the Bald or even with Louis VI the Fat and his brother with the help of his step-mother.
(Nice picture of Louis VI the Fat below)