Let's assume that our hypothetical ComedySystem is going to look a lot like DramaSystem through a different lens.
A lot of the character creation stuff would probably look the same as standard DramaSystem, with maybe a little tweak in the language here and there. Instead of a long-arc Desire that drives the characters, which probably isn't going to work in a setup that's essentially (static) situation comedy, we probably need each character to have a "Bit". That is, the part of the comedic glue they provide to the ensemble. Going back to our Brooklyn Nine Nine example, Boyle's primary function is as the loyal (even doting) sidekick to Jake, our cocky leading man, and by extension he's the nice guy who gets pushed around by pretty much everyone. We might call his Bit "Enthusiastic Pushover". Rosa might be a "Tough Girl with a Heart", Santiago is the "By the Book People Pleaser", and Captain Holt is the "Incredibly Serious Commanding Officer".
Supporting characters probably don't need much more than this - they're just there to do their Bit, like Scully and Hitchcock, who are there to be "Lazy/Incompetent/Gross Partners".
Dramatic Poles probably works as a measure for comedic characters too, but should be phrased in a way that we get a sense of what the characters look on a good or bad day. In a situation comedy, often characters trade back and forth who is the protagonist and who is the antagonist in the story; capturing a sense of what they look like when they're on either side of that line gives you some clarity. Captain Holt is a "Demanding Taskmaster" when the story calls for it, but a "Benevolent Leader" underneath it who really cares about his detectives.
Having the list of what the character wants from the characters in the main cast is still very important, because it captures a good deal of what the back-and-forth between them will be. The terms of those relationships probably won't change all that much, except at the end of an arc (when, for example, Jake might finally scrape up the courage to ask Santiago out). Knowing that Boyle is looking to Rosa, and later, Gina, for love and affection tells us all we need to know about the comedy beats that will happen when the two of them are in a scene together. Boyle asks them out (surreptitiously, if it's Gina) and they say no. Sometimes this rhythm can be broken up for comic effect, when Gina sees Boyle in a new light, or when Gina drinks too much and lets things get out of hand.
The rhythm of comedy includes Petitions, the same as drama, but I think that often the expectation is that Petitions will be denied. When Jake Petitions Captain Holt for approval, he's often in a position to deny Jake because he doesn't approve of his childish manner. The expectation of a Petition in a ComedySystem game is denial, I think, because it sets up a comedy bit; when Jake is called out for his childishness, it often makes him act more childish, like Daffy Duck. Maybe the rhythm is for players to offer each other bennies to be rebuffed, so they can push the button of their essential comedic conflict, but buy the Petitioner off when their intention is to change the rhythm up. Holt praises Jake for a job well done, despite the fact he's out of his depth "adulting". This could set up further bits where Jake is struggling to maintain Holt's respect, or Boyle is struggling to keep up his unlikely affair with Gina, despite the odds against it.
I'm still ruminating on this one. Will post more, or change this up, as it develops.