I am no where near as against it as others here, but at the same time, the end of part III was realistically the END. Mary died. that signified the end of the story. they all got theirs in that moment. Sure the time lapse to Michael's death leaves open possibilities but i truly believe when Mary was murdered everything came full circle.
If a Part IV were to be made i would only like to see it if they could in some way come up with an ending as close to satisfying as GF3, which may just be impossible. that scene alone almost won the entire movie an Oscar. I'm sure FFC could come up with something, but i just really love that ending. Also i would give top billing to DeNiro and Talia Shire. Give Andy Garcia and Franc D'Ambroisa supporting roles even Brigette Fonda. Then work from there. It shouldn't be Godfather The Next Generation. Focus on two of principle characters and go from there. if anything this movie should be a character study of Connie, Vito, and Vincent. at least then it wouldnt seem like a rehash of movie from the past.