Italy and Great Britain and/or France are, for whatever reason, inclined to be militarily and/or economically supportive of Greece during the Greco-Turkish war. As a result, the war ends in a Greek victory.

-Greece expands by annexing occupied territories, plus small bits on the Black sea with significant greek populations.
-Turkey becomes less independent as British and/or French and Italian forces maintain garrisons in the south of the country, expanding those two countries' influence in Asia minor.
-Armenia and the Kurds are granted their own states, although their stability isn't guaranteed.
-The population exchange still happens, but this time between not just Greece and Turkey, but between all four new states. (Greece, Turkey, Armenia, Kurdistan)
-Greco-Italian relations warm up a lot, Athens and Rome remain close.

How, from the point of Greek victory onward, does this change OTL? Don't bother rationalizing exactly how they won, other than if it would be the British or French (both?) who'd be more likely to support the Greeks, I suppose.

Here's the map I stumbled across that inspired this post.
PD8GV8g.png
 
Don't bother rationalizing [...] other than if it would be the British or French (both?) who'd be more likely to support the Greeks, I suppose.

OTL British foreign policy between 1783 and 1945 was to prevent creating hegemonic powers that could later control major trade routes. This TL gives Greece complete control of the Dardanelles, which would run counter to that policy (Worldwide free flow of trade was a major British foreign policy). Expect another Greek-Turkish War going similar to the OTL Turkish War of Independence and the Brits stand by hoping for at minimum Turkey recovering much of Greece's new Asian Minor provinces).

OTL Turkey stayed out of WW2 because it largely got its revenge in that Turkish War of Independence. Barring something similar ITTL, Turkey's fully in the Axis camp, threatening the Allies' Levantine protectorates in the next war (WW2 still happens in this TL) as well as the Suez Canal, which in turn imperils the British war effort.

Thanks to Megali Idea, the Greeks in the Italian areas (whom would be the plurality in the newly de-Turkified SW Anatolia) will want Enosis (union with Greece). Italy will not just give those areas up. Expect friction in the future between Constantinople (which was always meant to the capital) and Rome.

OTL Armenia was a Soviet SSR by 1922. If this TL means an independent non-Communist Armenia, the USSR's going to make sure it either makes it a puppet state or "unify" it with the Armenian SSR. There's no way that the Soviets are going to allow a possible irrendentist country on its borders. That also means the Turks (as enemies of the new Armenia) are effectively friends with the Soviets as in OTL.

OTL Kurdistan didn't arise because the Kurds were largely supportive of the Ottoman state. It wasn't until the OTL Turkish War of independence (which basically became a 'Turkey for the Turks' movement) and the Arab revolts where the raison d'être for a Kurdistan exists. But going with your TL, Kurdistan is actually the most stable.
 
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