Rogier,
First of all a late "welcome" to the boards!
I don't think that is a bad idea at all! I love that time period you are referring to and I think it would be interesting to tell a story of one of the other families. However, I don't think it would be a sequel to GF, which is probably good in the long run. I think it could possibly be another good "Gangster" movie.
I agree with WG, that we all love the Corleones and if their story has been told to completion, why not another good flick about another family? With the right actors/directors, who knows, could be a good movie.
TIS