Ala Forgotten Realms and other D&D properties? With Harriets approval I could see this being a great thing to continue plots and flesh out the world RJ created. Star Wars EU shows how this can be hit or miss (and incredibly messy canon-wise), but there are some incredible stories in there we never would have gotten without the freedom to do it.
I think its a good idea anyway, lets just not have his children (if he has any, I have no idea) do the writing. Dune is a great example of talent not passing genetically.