Why don't we imagine things that happened between Fredo's death and the fundation party?
After Fredo's death the family soon ran into a bedlam. Micheal was extremely agonized. Connie might soon know everything. Athony also caught some hearsay. But the family business went on. Micheal expanded his business to other parts of USA. He participated more actively in politics. And he expeled other mob families, men killed. But he successfully fool the media and public. After about 20 years Micheal, for the first time, failed to confound a plot against him. He was shot and he lost many men. Although he soon regained his power and position by savage revenge, Micheal didn't want to stay in the kill-and-to be killed world. He moved out and created the foundation.
Why don't contribute your ideas here and we can make a film between GF2 and GF3 out of our ideas here.

We have done so in bits and pieces. It's a long stretch of time and we can't be comprehesive without writing a script.