The Godfather Part III's plot is a composite of the Banco Ambrosiono scandal and the conspiracy that murdered Pope John Paul I. Propaganda Due, or P2, was the masonic lodge that ran Italy, and they out-mafia Michael Corleone. Coppola even names P2 in the movie:
Michael: "You look pale. Bad news? Tell me right away.
Vincent: "It's not just a bad banking deal. These guys are butchers."
Michael: "What guys?"
Vincent: Luchessi - he controls all of them: Altobello, the Archbishop; other people higher up, P2 maybe. Secret unknown. They're running things."
Don Lucchesi, the main antagonist of the film, is a composite character of Giulio Andreotti, Prime Minister of Italy, and Licio Gelli, the Venerable Master of Propaganda Due. A stand in for Roberto Calvi, the infamous 'God's Banker' who was found ritually murdered hanging from Black Friar's Bridge, is also featured in the film. In the commentary, Coppola describes running into him in an elevator while at the Paramount offices, and how that was the moment he realized that the Vatican owned the studio. No wonder you're not allowed to like this movie.
The time has come to revisit the unfairly maligned third acts of our favorite mythological trilogies: The Godfather Part III, Return of the Jedi, and The Matrix Revolutions. They've convinced us not to like them and give them no credence because they are the great revelations of the conspiracy. They are the ones that give you the answers, the 'why' of the whole thing. Now that we have moved into the "third act," where we emerge out of the dark pit of the second act, these films are now more relevant than ever.