I always imagined Santino Jr. being the legitimate son of Sonny who would want into the business.

And what would be more natural than Michael (Rizzi) Corleone, Connie's son (she would have dropped Carlo's name after his death), eventually working his way back up to replacing his own Godfather, Michael Corleone, as the Don??

Talk about coming full circle. In 1997, at the end of Godfather IV, Michael Rizzi "Richie" Corleone orders simultaneous hits on all his rivals (perhaps including his cousins Vincent, Sonny and Anthony?), which are carried out as he attends the funeral of Godfather Michael.

In the epilogue, in 2007, Connie Corleone dies, and Richie, now 58, is the only member of ANY of the extended families who attends her funeral. In fact, he's one of the only ones left.