Which Planescape Faction might Ranma (or others) join?

Just an idle little crossover thought... back in the 90s, Dungeons & Dragons released a setting called "Planescape", and a large part of the setting's unique vibe, inspired by TSR's rivalry with White Wolf, was the presence of in-setting social groups called "Factions". Often described as "philosophers with clubs" (I'm not sure if they mean social clubs or literal ones, personally), the Factions are organizations dedicated to pursuing what they believe is the true purpose of reality, partially by convincing other people that their philosophy is right and that by accumulating enough believers, they can MAKE it right. So, I'm contemplative; if Ranma (or any other recurring Ranma 1/2 character; Akane, Nabiki, Ryoga, Kuno, whoever) ended up in Sigil, is there a Faction that they might join? Hell, are there multiple potential Factions that a given character could find appealing? So, I thought it might be an interesting thought experiment, and frankly I'm curious about peoples opinions, so... here we are.

To make things a little easier, I'll try and summarize the philosophical viewpoint of each Faction, since that's likely the primary "hook" that a Faction would have to appeal to a Ranma 1/2 character, right? But I can elaborate on a given Faction if folks need more detail about how they operate and what they do.

Athar: The gods are frauds, who seek to distract us from the ineffable truth that as yet lies hidden, and which one must pursue to attain enlightenment.

Believers of the Source: Through trial and strife, one hones one's very soul. Each life is a chance to continue the forging, until one attains true perfection and ascends to godhood.

Bleak Cabal: There is no great meaning. There is no hidden purpose. The only truth is that which you can find within.

Doomguard: Entropy is inevitable. All things decay. Embrace oblivion.

Dustmen: The reality around us is a falsehood; we are dead, and doomed to false cycles of supposed reincarnation. Only by shunning all attachments and emotions can we attain a True Death and be released from this prison.

Fated: Strength is all, and desire is the root of strength. If you want it, take it. If you want to keep it, fight for it. You will only get as far as you're willing to take yourself.

Fraternity of Order: Reality works in accordance with a set of ultimate rules. By mastering the rules, one can control reality.

Free League: The Factions are loud-mouthed jerks who claim they know the one truth. They're all wrong. Be free, make your own opinion, and find your own truth.

Harmonium: One should seek the greatest good possible for the greatest number of people possible. The only way to achieve that is if we all work together to pursue it. And if people won't work together, kick their asses until they stop being a problem.

Mercykillers: Justice must be swift, pure, absolute, and final. Punish the guilty. Mercy is an obscenity that defiles Justice; shun it.

Revolutionary League: The Powers that Be are all corrupt oppressors, who shackle and chain us. Fight them! Make us free!

Sign of One: Reality is shaped by willpower and belief. Hone your will, and you will shape the world.

Society of Sensation: To know the multiverse, experience it fully. The senses form the path to truth, for the multiverse doesn't exist beyond what can be sensed.

Transcendent Order: Action without thought is the purest response. Train body and mind to act in harmony, and the spirit becomes ones with the multiverse.

Xaositects: Chaos is the ultimate truth of reality! All is Chaos; all is Chance; all is Whimsy! Embrace Chaos, and let whim be your guide in all things!