Note: SIU has yet to use any specific term to refer to these families as a single defined classification, so we shall refer these families as "Special Families" due to their influence within the the Tower.
Special Families are Families which likely hold some influence in the Tower and are special enough to be awarded privileges or if not, special contracts.
Special Families are different from ordinary residents of the Tower such as Ship Leesoo's family or Hatsu's family, as their amount of political influence or privileges, set them aside from the common class. However, they are not part of the nobility or the ruling class such as the Zahard Family nor the 10 Great Families. However, they differ from the common people residing on the Tower.
Apart from the 10 Great Families, the other Special Families probably operate with the knowledge and also, the blessings of the Zahard Empire. This is assumed on the basis the Zahard Empire controls how contracts and even Special contracts are given out. It is unknown if certain Families also serve the Zahard Empire in exchange for these privileges and other benefits.
Special Families may possess special/unique techniques, physical traits, contracts or special items. As such, several families have managed to obtain special contracts with Guardians that give specific bonuses. For example, the Mule Family holds the "Iron Man" contract. It is a contract for the Mule Family that regenerates the user's stamina.
It's unknown what surnames some of these derived or branch Families use. Though it seems Laure uses the Phonsekal surname, it's possible his surname is actually Eurasia. Marriage between other Special Families may occur as well and they may even have derived families too.
A person can be adopted into a Special Family and it is likely only a specific few are chosen to be adopted for a specific purpose.
For example, Androssi Zahard was adopted into a branch Family because she showed combat talent, as the branch Family was desperate to produce a Princess so they wouldn't be exiled. Another example is a Ranker being adopted into the Zahard Family to maintain and uphold a set of rules.
After a person has been adopted into a Family, they may receive privileges and so on, in exchange for achieving certain purposes for the Family.
If a person born into a Special Family has been adopted into another Special Family, they may retain their privileges and special contracts from their birth Family. The Special Family they've been adopted into is viewed as their post-Clan. However, in return for bearing the crest of their post-Clan, they probably lose the right to bear the crest of their birth Family. Examples may be Yuri Zahard and Lo Po Bia Ren who don't wear items bearing the crest of their birth Families.
It's unknown if any of the 10 Great Families allow their members to serve another Great Family.
Known Special Families
Other possible Special Families
These families may be special, since they have a known family member, with rather a high Ranking and influence. However, their status is not confirmed as of yet.