Start with the founder, and assume no more than two heir-candidates per generation. Fairly standard stuff. But with each generation, each heir-candidate gets played. The result is a very fleshed-out family tree. This would be way cool, but also a nightmare for record-keeping and also finding enough people to take on heirs.
Gen 1/Founder: laridian plays the founder, who has two heirs, Adam and Anna.
Gen 2: madame_ugly and pixelcurious play Adam and Anna respectively. Adam has two heirs, Betty and Boopsie, and Anna has two heirs, Beanpole and Barbara.
Gen 3: seidoo_ryuu plays Betty's story, amaryssobellus plays Boopsie's, iceraptoress plays Beanpole's, and simtarts plays Barbara's.
As you can see, by Gen 4 you would need eight people, and by Gen 5, you'd need sixteen different players. Even assuming the earlier people would be willing to do another later generation, that's still a lot of people.
This is why there's no chance of going to Gen 10, as I'm sure you can see. The progression would double at each generation (assuming I'm doing the math right - if not, please correct me), leading to 512 different Gen 10 stories. There might be a few hardy souls willing to go that far, but 512 of them? Never mind trying to read all of them. Even five generations proves to be an awful lot.
Let's not even think of adding in any non-heir siblings...