Just as changing the game attributes for an individual reflects a particular conception of how this game conceives of people and what matters about them, I think the same is true of organisations/groups.
Oh absolutely. I picked the things I picked, and framed them as I did, because I was envisioning groups in a particular way. To be accurate, I was envisioning
portraying groups in a game in a particular way. Although doubtless informed by my own bias/beliefs about groups and society I was aiming for mechanical options that would allow players to game them rather than "realistic" modelling. And always with eye toward drama.
Another thing that has occurred to me is who gets to define (however one wants to do that) a group and when? Player? GM? Group Consensus? Are they defined before game start? Can they be defined during play by player activity?
Ideally I would want a session 0 where all players to sit down and throw ideas into the ring which are then chosen by group consensus. Then, during play, players could define new groups as they wish and as allowed by the games mechanical options.
Example: At the start of play
Battleship Potemkin includes 3 groups* - the working class, the aristocratic class, and the military. The Potemkin has on board of it members of all 3 groups. Early in the play, in reaction to something that happens,* a player decides that the crew of the ship should be made into a group. The player/PC takes actions to create/activate the crew; perhaps they make an oratory skill roll, perhaps they spend a plot point, maybe it's a play in their playbook. The Crew of the Battleship Potemkin is now defined as a group and can be utilised in play as a game resource.
How the player defines it leads to different ways for telling the story and the mechanics for same. So, if the player's original definition of The Crew of the Battleship Potemkin includes "all sailors aboard the ship, including aristo officers" is it more difficult/cost more game resources to activate the group than if they just included the working class sailors? I think most of us would say "yes" to that because for the aristo officers to be included they (the officers) would have to be convinced to work against something that is an interest of their first group, the aristocracy. Alternatively the player may decide to exclude the officers, making it easier to create The Crew of the Battleship Potemkin but leading to the question - what to do with the officers? Do the sailors throw them overboard? Do the officers simply flee?* And where in the game play does one include the purging of the crew? Is it simply an included part of the creation process, hand-waved away with a brief description, or do we focus the play on the specifics of the mutiny with all the sneaking, the quiet violence, the reprisals, of removing the officers? You get very different stories depending on what you choose. (IIRC the movie opted for the hand wave, it wasn't telling a story of cloak and dagger but of class unity.*)
As complex as my example is so far I'd like to bring in another dimension: the military. At start of play each individual aboard the Potemkin is a member of 2 groups, their class and the military. The Crew of the Battleship Potemkin mutiny against the military. ie. they leave that group. What does this entail in game terms? Is there a Group Cohesion stat that the player must overcome to break the crew away? If not what other issues might there be to make this dramatic? Maybe they
don't break away from the military. Maybe they continue to think of themselves as proud Russian Navy sailors, loyal to the Motherland. They act as they do in order to protect Russian people (and the Russian People) being more loyal to that interest than that of following orders.
I'm reminded of the Spithead Mutiny, a naval mutiny among the British navy during the Napoleonic Wars. The mutineers were demanding better pay and conditions. They kicked the officers off the ships and refused to sail. BUT the mutineers guaranteed that, if the French fleet were to set sail, that they would sail in defence of Britain. These mutineers had goals, better pay and conditions, and interests, national defence that were at odds. A gamified definition of this might be that the Spithead Mutineers were activated as a group that was still contained within the larger group, the British Navy.
BTW. I'm not suggesting absolutes, just options that can be considered. To repeat what I said in my previous post, how far down do you want to dig? How much detail do you want? How much do you want intersectionality to play a part?
* I haven't seen the movie in decades, details are fuzzy.