In BE the term is "great family," and it means a nexus of surnames that goes back to some notable event conferring status-- usually the Norman conquest of 1066, but certainly many Great Families came into being via other political upheavals, such as the War of the Roses and the Puritan Coup d'état of 1642.
So in your terms, a large number of family members isn't the point. It's their history and pedigree, and a status inversely related to the capacity of blood cells to carry oxygen. (Meaning he blood of great families is not robust and red like yours and mine, it is blue.)
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