Might as well have the Corleone's find Osama Bin Laden at this point and give him a Sicilian neck-tie...

I hate to say it, but the Godfather stories have all but been maxed out. They've pretty much used all the themes that would be used in a Part IV, fall from grace, loss of innocence, getting pulled back into the crime world, lost love, lost family, etc...

The only thing that I can see would be putting a nail in the Corloene family's coffin. Just tear the rest of them apart and kill them all off. Cap the film off with a shot of the family from Connie's wedding.

It's getting to the point of "why bother?", but it is fun to try to come up with a good reason for a Part IV.