personally i don't think that they should make another film to add to the trilogy because that will ruin it. a trilogy should never be expanded on. i think that if something has to be done then it should be a whole new trilogy to stand alone (like star wars).

1.this could either be set after godfather 3 with vincent and possibly some sons of his own and their story set over a trilogy.

2.or you could have a trilogy of prequels set before godfather 1 showing the families rise to power in america, this way you could use deniro again.

3.you could have a trilogy of films to plug the gaps.
part1-set between deniro's final scene in part 2 and the first scene of part 1-showing families rise to power.

part 2-set between part 1 and 2 showing how the family settle in nevada and how clemenza dies and expand more on michaels relationship with roth.

part3-set between 2 and 3 showing families move to legitimacy, tom's death and emergence of joey zaza.

this would be most difficult as all original actors would have to be replaced.

why 3 movies?

why not just one, to start with...

a prequel trilogy would probably be about Antonio Andolini, the young-Vito scenes have been done already.

your third option is quite original, I must say, but that one does add to the trilogy, I would say