No meaningful genealogical information is known for the 7th - 10th Dynaties. The 7th/8th Dynasty kings are thought to be descendants of Pepi II of the 6th Dynasty but even this is conjecture. Five kings of the 7th/8th Dynasty have the throne name of Nerferkare, which was also that of Pepi II, so this looks like at least partial redundancy. Nitocris of the 7th/8th Dynasty was a female pharaoh and perhaps corresponds to one of the several powerful queens of the 6th Dynasty named Ankhesenpepy.
The 9th/10th Dynasty is thought to have come from the area of Herakleopolis near the Fayoum in Lower Egypt. As many as five kings of this dynasty have the name Khety/Akhtoy. Most have throne names ending with -kare, so perhaps a few of these were the same king using variations of the -kare prenomen, i.e., more redundancy.
Also note the pattern of kings named Pepi in one dynasty and kings named Akhtoy in another. This pattern was repeated at the beginning of the New Kingdom when there were pharaohs named Apepi (Apophis) and Tao. So, perhaps the 9th/10th Dynasty is just a local (Herakleopolitan) version of the 6th Dynasty list. The 11th Dynasty is thought to be primarily Theban, which again points to redundancy with lists of kings from other regional sites.
There is only one or two kings that have the element -ibre. This made for a ready pun with the Hebrew eber. However, we can disregard any propaganda about foreign/Asiatic invaders of Egypt other than one prince libeling his brother as such. All of these royals lived double lives. They spent part of the year in Mesopotamia and "sojourned" in Egypt for the winter.
© Charles N. Pope, US Library of Congress. All rights reserved.