Serpent
Banned
I can not see why would the Greeks spend money an manpower to fight in the Suez Crisis. It is not like UK and France need military help either way. They are 2 of the Great Powers with massive militaries so what would Greece offer? Also that crisis is one that both USSR and USA agreed against it so I can't see how that will help the case on Greece helping the declining Imperial powers.
Greece has both the logistical capacity and an ideal location to support the Franco-British in their Suez intervention. That being said, the more powers/forces involved in this affair, the harder it would be for the Franco-British to pull out, especially before fullfilling their stated objectives, which would happen much earlier with Greek (& quite possibly Spanish) military assistance.
Also what is this craze with Israel? Greece has it's own problems to fight in the Balkans or in the EEC to intergrade towards the lucrative western markets for better economic growth rather than a region which is truly unstable OTL. ITTL we could even see a united Arab kingdom which is even British related so we could see 2 possibilities:
1) The British push the Arabs to accept the Jews as an exchange for something the Arabs want. 2) The Arab front being united under 1 government it could throw the Jews out before they entrench themselves in 1947.
Personally I see 1 as more likely but ignoring a more stable Arab world ITTL and it's relation with Israel. Also I still can't see why would Greece entangle itself in that mess either way. I can see them trading with Israel of course even selling weapons but I can't see them sending troops or even embargo the Arabs as the more markets to trade the better and also the more stable situation the better.
Greece's interests would be disserviced, if the political leadership were to involve the nation in significant manner in a pointless bloody & prolonged conflict in Yugoslavia. Then you have Albania, which doesn't really need a large chunk of the Greek Armed forces to deal with. On the other hand, you have (Greater) Lebanon, Assyria & the Nile Delta+the middle Nile, where most of the Christians (5+ million) in the Middle East are located, including some 500.000 Greeks. It is more than apparent which region would take priority, both in the eyes of the Greek public, as well as the considerations of the Greek leadership.
About full Turkish occupation ITTL, I can't see why it would happen. Unlike the Asia Minor Campaign airpower is way more important here and can subdue Turkey way easier than occupying every part of the State. If one combines the breaking of all 3 fronts with a continuous air bombardment I see a very likely scenario where there is a riot against the government especially if the Allies give generous peace terms if minimal ground changes. I can see this happening in early 1944 so the Allies can free a lot of their troops towards the main enemy. Of course a full occupation might occur I just don't think it's the best on the Allies sides. Every division in Anatolia is not a division defeating Germany.
Your misguided premise is based on the notion that the Anatolian front will be wrapped up by early 1944, and/or that the Turkish leadership would be totally willing to surrender, (and lose their heads), rather than fight it out to the bitter end, alongside Hitler. Given Kemal's legacy, you should very well know that the answer would be the latter, the Turkish leadership will never accept defeat, not unless they're fully occupied.