Great question!
For a single domain run by multiple players, I'd split the stipend, decide jointly on the projects, and decide which player the drama is about each turn by rolling.
That said, you could also give each player a "specialization" within the domain, and the ability to pursue individual projects related to their specialization each turn. For example, one player could be a spy-master, another the architect, another a court wizard, and another the military strategist. This solution has benefits and drawbacks: the main drawback is that each player isn't making as much gold, but the benefit is that they can individually pursue a lot more projects.
And of course, the last option is to just give everyone their own village and make them all Lords and Ladies in service to the king. For added intrigue, have each player inform you of their seasonal actions via a private message or post-it note. They may also send one additional secret note to another player each turn, and may make a public announcement about their intentions. Of course, with the addition of some NPC nobility plotting their own schemes, you'll soon have a system that will kill friendships as surely, though far more subtly, than Monopoly.
Let me know if you have any other questions!