Joseph doesn’t have to be a group. The story that takes up most of the end of Genesis is plausible and coherent read as straight history. There is no need to interpret Joseph as a composite; but there is an advantage.
The descendants of the Abraham Group reacted badly, even criminally, to the series of minor droughts and famines of the time. They cheated and warred with each other, even selling their own relatives into slavery. They were not far removed from generations that practiced human sacrifice, and the whole depressing mess with Lot, Jacob and Esau, Laban, Rebecca – the whole crew, really – is a collection of unattractive characters, only intermittently faithful. I will handle that group on its own, but for now it is enough to remember that God choosing that group must have seemed pretty unlikely to everyone around, including the family itself. No one seems to get along, and tribal loyalty is an obligation everyone tries to get out of and abuse if they can. This bunch is not reminiscent of great conquerors and wise men from the east, but of those families that used to live on the edge of town, like the Herdmans. Outsiders can't tell whose kids are whose, and cousin-marriages aren't out of the question. The police are always coming because they're always fighting, and they leave junk around everywhere. Clearly, they were not chosen for their good qualities, but to illustrate God’s good qualities.
But they must have had something going for them, because the Joseph group, sold into slavery or arriving during famines like refugees in Egypt, managed to prosper and move into positions of authority. Even though we don’t have independent historical evidence for any Josephs who really wowed the pharaohs and ended up second-in-command, it’s quite possible. Even if the story is meant to be read as a composite Joseph, the elements are there: remain loyal to the god of your fathers, do not sin, the Lord will bestow wisdom and knowledge on you. You will not only survive, but prosper in the new land. You will be a mystical people of dreams and understanding. Stick together, sacrifice for each other.
The Joseph story teaches that favoritism among multiple wives and children is a dangerous thing, that sexual sin is a great dishonor to yourself and to others, and that lives can rise or fall on a single act of obedience or disobedience to God.