The Kisaragi family are the second family of the Duodecim. They place no importance on bloodline and all that matters to them is one's abilities.
They were formed by Seven, one of the Ten Sages. It's presumed he is still their patriarch. Jin Kisaragi belongs to this family.
As the second of the Duodecim, the Kisaragi family is known by the other families of the Duodecim as extremists who border on being mercenaries. This is largely in part because of their tradition of ignoring bloodline and relations in favor of solely the talents of their members. Due to this, the Kisaragi family is nothing like a traditional one and contrasts greatly with the Yayoi family; despite this, the two families remain in good relations with one another and the Novus Orbis Librarium. The other Duodecim, however, do not view the Kisaragi in a positive light.
The Kisaragis obtain talented children across the world through unknown means, and give them both an advanced education and training in combat before sending them to the Military Academy. One's origins play no part in how they are adopted.  It is because of this that the Kisaragis produce a high number of quality soldiers for the NOL. The nature of the family has also led to internal power struggles, and some members have hired assassins against others. Jin was noted to be a frequent target of assassins like Shiori Kirihito in the Military Academy since he was presumed likely to be the next head of the family. For this reason, Taro Sasaga'e was secretly positioned as his bodyguard. 
Just as the Yayoi's history is entangled with the Sealed Weapon Izayoi, so is the Kisaragi's history entangled with the Nox Nyctores Mucro Algesco: Yukianesa. Seven was its first wielder, who used it to kill Eight and then hid it while claiming that she had stolen it. Afterwards, the Kisaragis somehow lost the weapon, but it returned to their hands when they adopted Jin, who was found wandering with it.
They agreed to aid Kagura Mutsuki in his coup d'état against Izanami, hoping to put Homura Amanohokosaka on the NOL's throne.
BlazBlue: Central Fiction Library Entry
- Kisaragi Family
One of the families of the Duodecim. ‘Kisaragi' means ‘the second moon.'
They attach no value to bloodline or social standing. One's abilities mean everything in this family. They gather talented children from around the world by various methods, and train them thoroughly in combat.