Turkey needs a bigger population and more territory.
- The Mosul Question ends in Turkey's favor, with the Mosul Vilayet going to Turkey.
- The Turks and Soviets have a population swap of Armenians and Turks where the Soviets send all of the Azeris and Turks in the Caucasus to Turkey
- Greece sends its Jews and Albanians to Turkey in the exchanges (both considered OTL)
- Yugoslavia sends its Turks and Albanians to Turkey (repeatedly considered OTL)
- France, in its desire to woo Turkey away from Germany, cedes Syria east of the Euphrates along with Hatay Province
- During WWII Turkey joins the war on the allied side, claiming the Alawite State and the Dodecanese for itself. Britain also promises Cyprus to Turkey and delivers. Rump Syria, meanwhile, is a Turkish-dependent satellite state which relies on Ankara for water and access to the sea.
- Control of Northeast Syria and Northern Iraq also means Turkey controls Iraq's water, so Iraq also tends to follow Turkey's lead on things.
You've now got about ~180m people present-day under Ankara's sway directly or indirectly (About 120m of which is in Turkey itself), lots of oil revenues going to Ankara, and a military presence stretching from Basra to the Bosphorous.
After the Cold War, Albania and Bosnia also swing into Turkey's orbit.
EDIT: Turkey also brokers peace deals for Israel where its soldiers are stationed in the Jordan Valley and in Northern Sinai, insulating Israel from any threats to its east and west, but also serving as a means for Turkish power projection. Plus, as a symbolic matter, Turkey gets a status as protector of Al-Aqsa, which provides a soft power boost.