From the writing side, you can see a path where they may have started talking about the Vatican bank and the death of John Paul I as backdrops, and then came up with this European company as a vehicle to tie the Corleones into similar events.

I've seen proposed a progression, from the first movie being essentially local, to GF2 being national in scope, and GF3 international. If that's intentional, then GF4 seems inevitable, as space gangsters would just be too cool.