Sorcerer Families (術師家,Jutsushi Ke?) are clans of jujutsu sorcerers where the majority of members can utilize jujutsu. Sorcerer Families are prominent figures in the jujutsu world, especially the Big Three Sorcerer Families (御三家,Gosanke?), who hold the most prestige and influence.
The three great sorcerer families of the jujutsu world are the Zenin Family, the Gojo Family, and the Kamo Family. They appear to descend from the Big Three Vengeful Spirits (日本三大怨霊,Nippon San Dai Onryō?) of Japan, each of whom were powerful sorcerers of the Heian Era, the height of jujutsu sorcery. Due to this and the powerful cursed techniques passed down through their clans, the Big Three Sorcerer Families have gained great political prominence in jujutsu society.
Each of the big three sorcerer families has information on the other, and the word gets out on their inherited techniques. There is a struggle for dominance between the three families, as well as genuine bad blood. The Zenin Family and Gojo Family heads clashed at one point in the past and killed one another, starting what would become a feud between the two families. The current head of the Zenin Family, Naobito Zenin, has stated he wouldn't mind the Gojo Family going out of power despite Satoru Gojo being the deterrent from curses taking over Japan.
There are various other sorcerer families as well, such as the Inumaki Family. They possess an inherited technique as well and while not respected on the same level as the big three families, they are still well recognized by sorcerers.
The Zenin Family and Kamo Family especially value blood ties and the ability to use inherited techniques above all else. The Zenin Family are known to reject those without quality cursed techniques and in certain circumstances, such as with Megumi, are willing to pay to introduce those with inherited techniques back into the clan. Despite being an illegitimate son, The Kamo Family reluctantly raised up Noritoshi Kamo to be the next head of the clan because he possesses the inherited technique.
Big Three Sorcerer Families
The Gojo Family (五条家,Gojō Ke?) descends from Michizane Sugawara, a legendary jujutsu sorcerer from the Heian Era who became on of the Three Great Vengeful Spirits of Japan after death. Currently, the Gojo Family is just the one-man presence of Satoru Gojo, the world's strongest sorcerer. Their primary inherited technique is the Limitless along with the Six Eyes, the most powerful jujutsu. Thanks to Satoru's prowess the Gojo Family currently sits atop the jujutsu hierarchy and maintains the balance of power. This allows Satoru to act selfishly and impose his political power to save sorcerers like Yuji Itadori and Yuta Okkotsu against the wishes of more conservative sorcerers from the other families.
The Zenin Family (禪院家,Zen'in Ke?) embodies the nobility status granted to them as a major clan. They value powerful cursed techniques above all else and reject their own family members if they don't deem their power acceptable. Even Toji Zenin, as powerful a fighter as he is, found himself rejected by them due to his lack of cursed energy and left the clan, even changing his surname.
In a similar situation, Maki Zenin also left the clan to become a sorcerer and spite them. The Zenin Family still actively tries to prevent Maki from receiving a promotion in her sorcerer rank. Maki's twin sister Mai Zenin was also ostracized by the family. Despite possessing a technique, Mai is a girl so "perfection" is expected of her unlike the male members of the family.
Toji's son, born Megumi Fushiguro rather than Zenin, was initially raised outside the clan, but the Zenin Family was willing to pay top dollar to reintroduce him back to the clan. Megumi was born with the Zenin Family's celebrated hereditary Ten Shadows Technique. Under the protection of Satoru Gojo, Megumi was brought into the clan and eventually made his way to becoming a student at Tokyo Jujutsu High. Megumi claims to have no connection with the Zenin Family any longer.
Naobito Zenin was the current head of the Zenin Family. He embodied the aforementioned ideals of the Family in addition to its long-standing dislike for the Gojo Family. In his will, Naobito left everything to his son Naoya, who much like himself, embodies the problematic traditions of the major clans. Eager to become the head of the family, Naoya openly welcomed his own father's death. However, in Naobito's will, there is a clause that states if Satoru Gojo is incapacitated for any reason then Megumi is to become the heir. Trapped in a struggle for political power, Naoya doesn't hesitate to decide on killing Megumi.
The Kamo Family (加茂家,Kamo Ke?) values blood ties immeasurably, but like the Zenin Family, inheriting their passed down technique is first priority. Noritoshi Kamo was born to a mistress mother, who was mistreated and never accepted by any member of the family. However, Noritoshi was born with the Inherited Technique of the Family: Blood Manipulation. An ability praised for its overall balance and its perfectly suited to people who value blood. The true wife of the head of the family could not bear a son that inherited the technique, so Noritoshi was chosen to become the heir. In order to protect his mother, Noritoshi feels pressured to behave in a way befitting of the clan.
The Kamo Family is also responsible for the biggest blight on the Big Three Sorcerer Families. Recognized as the evilest sorcerer in history, Noritoshi Kamo of a past era performed experimentations on humans and cursed spirits that essentially resulted in the Cursed Womb: Death Paintings. His own blood was added to the mixed DNA of the original parents of the Death Paintings. When numbers one to three were incarnated, they possessed innate techniques that revolved around using their own blood.Choso in particular was inherited Blood Manipulation itself and is superior in using it compared to Noritoshi the student.
The Inumaki Family (狗巻家,Inumaki Ke?) is one of many minor sorcerer families. Despite not being considered a major clan, the Inumaki's Inherited Technique: Cursed Speech is well respected. Its recognized by the Inumaki Family sigil, the "Snake Eyes and Fangs" emblems born around the mouth of a cursed speech user.
As a first-year student, Toge Inumaki was the highest-ranking at Grade 2 (before Yuta Okkotsu joined the class). He was allowed to take on solo missions and the inherited technique was considered strong enough to deal with most instances. As a second-year, Toge is well respected among all his peers, even the Kyoto students who fear him the most out of any of the Tokyo Team during the Goodwill Event.