Whatever happened to Vito's grandchildren:
Vincent, s/o Sonny
Connie's sons (Michael mentioned them when she wanted to remarry)
Sonny's children by his wife: the twin daughters and young son (shown when the wedding photo was taken), and infant his wife was holding in the original movie while standing in the kitchen after Vito was shot?
Michael's son, Anthony
Tom's son, Andrew
A sequel could be derived to include these individuals and their adult lives.