Takemura Kouka, Matriarch of the Aiki Consortium, a Direct Family of the Amaya-kai
Akiyama Yoko, Former Captain of the Aiki Consortium
When you're a magic-themed crime syndicate, having a bunch of people who happen to be experts in magic is probably a very useful thing. What is directly known about the group mostly involves the ceremonial functions they serve. They say that it is the Aiki Consortium that discovered the power behind the spirit ink, or that they empower it in some way. (This explanation ignores the fact that the Osato-kai also have spirit ink tattoos.) Rumors abound that every member is a hanyou, child of a youkai and a human. Mysticism and misdirection are a way of life—and they're not even the spy Family here. They have a very close connection with the youkai and kami and serve as the PR on that front. While it's not as well-known since the existence and reality are not greatly advertised, they understand the Hellmouth functioning and are the main force that helps defend their Clan, Japan, and, as an extension, the world from the evil that would seek to escape and destroy. Most other Families only deal with the stragglers that escape to cause chaos in the mortal plane and don't fight the demons on their home turf. Even when other Families in on the secret serve as the muscle, they are the tacticians and guides. They do engage in a bit of blackmail and assassination, but unbeknownst to most, they only target shapeshifters and the like that have used their powers to gain a place in society and hurt others.
Some of the rituals are not very intricate—they help formalize the passing of leadership to a new Matriarch or Chairwoman, and they acknowledge the creation of a Family, no matter how small. On the other hand, it is required for them to help the ritual to bring back one of their own from the dead, a dangerous affair that does not always succeed. (It is required to try to bring back a Chairwoman, despite the risks, and most Matriarchs are also prioritized.) While magic is used for healing by many other groups, the precise, ritualistic methods the Healers use were definitely constructed by the Consortium. (This one isn't mere boasting. The Osato-kai favor a sacrificial type of healing magic--blood magic--possibly derived by observing oni, but it's not evil.) Whenever there's an unknown curse or magic at work, they are the ones you go to. They write the guides to demons and the like, and consult. Most don't like visiting them any more than they like visiting Akiyama, though, feeling like there's an uncomfortable aspect of any member of the Consortium being able to read their every thought.
The jealous spread rumors that the Consortium are actually an attempt by the youkai to take over the functioning of the Clan. They use the Consortium's vague answers and lack of explanations as proof of their misdeeds. And, of course, they aren't in the habit of defending themselves, even against such insults.
The few known facts are very small and straightforward. The Aiki Consortium is definitely one of the oldest Families in the Amaya-kai, if not the oldest Family. The good relationship between the Amaya-kai and the youkai, parallel to the Osato-kai's relationship to the Oni, is all due to them. The Matriarch always enjoys a vast influence on Clan affairs, though they rarely throw around their weight or ascend to the position of Chairwoman. Despite this, they tend to like to sit back and watch affairs, only stepping in if they feel it's necessary.
It is not entirely true that Second-Tier Families are never promoted from the Aiki Consortium, but it is relatively rare, and none of the Amaya-kai still living remembers an instance when it happened. It's caused quite a commotion and rumors about Akiyama, but she's been quiet, amused, and mysterious, which is fairly in character for a former member of the Consortium. The consensus came out that some sort of prophecy required its creation, but the actual truth—that Akiyama distinguished herself while fighting demons inside the Hellmouth—Is not one that is told. (And, since Takemura never fully explained her reasoning to Akiyama, Akiyama herself speculates that there's also some sort of prophecy Takemura isn't sharing.)