I think that a Part IV would have to take a hard line showing Vincent saving the family or ultimately destroying it by inexperience or a crucial mistake.
I personally would rather see him restore the family to power by doing a deal on his own while Michael exiles himself in Sicily.
I don't like the idea of any of Sonny's other children involved in a power struggle since they have likely been sheltered from the mafia life since Sonny's death.
I also like bringing Anthony back into the mix and ultimately have him become a part of the family as well. If there is to be a power struggle, I think it would have to be between the two of them, since Anthony is sure to partly blame Vincent for Mary's death.