In the world of spying and intrigues there is still much opportunity for adding spice to the game.
(1) You could appoint trusted people, confided agents, whom you send to any person in the game for spying on him/her and revealing information useful to you. It is hinted at already by events, but I am thinking of a more direct way to produce evidence. Not connected to your focus on spying, as it is their talent which counts, not yours. And the use of this evidence could also be fine-tuned - for blackmailing cash, for forcing them to 'do you a favor' or demanding their altogether retirement from political involvement (so to say abstain and keep to a private life - but this requires very serious evidence like high-treason), or renounce a participation in intrigues and factions.
(2) You could order your courtiers to do things for you. Like seducing the wife of your opponent for causing him trouble in the family. Like hiring thugs over them for kidnapping his family members and asking ransom. Or simply having them sold to foreign slave traders. Or putting them by force into a monastery. That would bring you into some dependence of those courtiers, because they could threaten to tell that what they did for you once to others, as well, or change sides if you don't keep them happy. Depending on your espionage skills, you could handle a number of such personal agents. The element of fear is here also a thing that needs to be implemented. Use your personal agents for intimidating vassals, so they abstain from opposing you. Could work, or could make them join factions against you. This concept means adding a value to your court members you rather neglected in the past. Personal traits will become more important in that court, as it will become a pool of skilled agents for you. [edit:] To make that even more interesting, you may also spy on your spies just for testing them if they are honest with you or also work for somebody else - worst if they are double-agents for you and the fiend alike. Tricky grounds!
(3) You could use confidants also for positive things, like negotiating a deal between hostile houses. Settle conflicts in peaceful ways. This would earn you gratefulness of the parties, while you have to do salomonic decisions sometimes, finding a compromise in their clashing demands. Also could be used for proposing marriages and political pacts between third parties.
(4) You could propose a crusade against target region you specify in a message to the Pope. Maybe would need to be connected to a promise to send certain number of soldiers for that task and other benefits like bounty for the Church. Needless to say that region needs to be of non-Christian faith to be legitimate, preferably Muslim or pagan/heretic.
(5) I think there should be something like a 'King Arthur round table' where you assemble your most trusted vassals, courtiers and even foreigners for sort of an elite group within the realm based on personal friendship and shared ideals of chivalry. The members of that group will be most loyal to each other and you should be able to ask them for help in times of trouble. Troops, money, influence on troublesome vassals... [edit:] means also you have duties to them or they leave the round table/cabinet intimate club being disappointed. Belonging to this chosen few should mean high prestige for members. To get thrown out a substantial loss of prestige.
(6) Let's add some ways of calming down rebellious spirits in your realm by public events where you donate for projects like new cathedrals, hospitals, charity work or fine-tune taxes and contributions for single vassals. You may also build things for them benefitting them like royal roads through their territories or you grant rights to his towns to hold a fair which achieves an international fame and brings him advantages. Of course his gratefulness is expected in return.