Just re-read intrigue, and I'm coming away with a few questions.

1. Should intrigues have a limited number of rounds, based on the length of time possible for the scene? RAW, Intrigues run for an unspecified number of rounds, but Social Objectives (or definitive failure) can be used to indicate that a scene should be over. It seems like Intrigues could just go on forever, which kind of takes the power out of Rhetorical Points; assuming no one is competing for a Social Objective that would negate yours, couldn't you just take as long as you want to accumulate all the Rhetorical points you need? At that point, why use them?
2. Has anyone used Intrigue for particularly long social situations? Like multiple days or weeks in court? Is there any reason why that shouldn't work? Or is Downtime better for that? (Seems like Mass Battle can be used for days or weeks of war, which is why I ask)
3. What if a character decides to change Social Objectives based on new information revealed during the scene?
4. What if one PC completes their social objective before another? Are they stuck with assisting? Or can they take a new one?

I do easy Intrigues with no limited time frame, and when I want players to GET TENSE, I introduce a clock limit. I would suggest mixing it up, doing a good balance of both.

I roll with the home rule that you get to change your objective for free after finishing the previous one and that you can swap them at will even before that, but this may erase accumulated rhetorical points.

Gotcha. Thanks! Do you then just have NPCs do a Use Skill action to determine their new objective? (Since that's normally done in Assessment)

I allow to ditch/switch an objective at end or start of your turn, before or after the action is made. My current ambition is to make an Intrigue challenge spanning an entire night, with multiple objectives to accomplish (each tracked separately) and limited number of turns to do so, with each turn representing a certain "slice" of night.