You should add somthing about the byzantine empire in the facist tree. Maybe start with taking turkey, bulgaria, islands italy holds. That'd be noice

Claims to restart the Macedonian Empire.

All those above sound good for a fascist branch, but I'd also like to see a democratic branch, focused on defense (maybe with an event with the UK giving them Cyprus?) and a communist branch, focused on cooperation with the USSR and conquering the straits (via ultimatum to Turkey) and lower balkans (Albania, Macedonia, and Bulgaria).

Maybe a nonaligned tree leading to forming a balkan faction to make Greece friends with yugoslavia and romania opposing Italy? Maybe with a late option in that line to demand eastern thrace from Turkey?

For Neutral Greece I think should be about forming Factions through alliances and fortifying the Metaxas line
For Fascist Greece I think it should be about Axis collaboration or conquering Balkan states
For Communist Greece I think there should be an alliance focus with the USSR and maybe spreading communism by befriending balkan states
For Democratic Greece I think it should be join the Allies and closer ties with Britian and France