This isn't as hard as one would imagine. Turks have been living in the Balkans since the early 14th century and this increased when Tamerlane ravaged Anatolia and forced many Turks to cross the Dardanelles and settle in OTL Bulgaria and Greece. There was so much Turkish migration that the Muslim population (indistinguishable from the Turks) constituted 43% of the population in the Balkans, particularly in Bosnia, Kosovo, Albania and eastern Bulgaria. Intensify this by perhaps deporting OTL unruly Muslim populations like the Alevis to the Balkans (maybe expand it to deporting the Alawites of Syria who resisted Ottoman attempts at conversion to Sunni Islam). Same thing applies to the Greeks and Slavic Christians: they revolt en masse and the Ottomans decide to deport them to Greek Anatolian areas like Cappadocia and Pontus.
In OTL, there was overcrowding in the Greek islands in the Aegean and many migrated into western Asia Minor, increasing the Greek minorities. Given that western Asia Minor would be a TTL dumping ground for the Ottomans to throw uppity Greeks, said migration might cause the Greeks to become a majority in western Thrace. Should said Ottoman Empire still survive in a stable condition, they have resources that they could exploit and jumpstart an Industrial Revolution (coal, iron, wood in Bosnia, light textiles in Bulgaria, etc.). You would have Greek and Armenian capitalists in Constantinople and Asia Minor financing the building of Ottoman factories and railways. Due to foreign governments like Russia exploiting the plight of Christian minorities compounding the existing distrust the Ottomans had for them, the government encourage Anatolian Turks and Arabs to migrate. Think of it as the Ottomans' counterpart to the Great Migration - millions of Muslim laborers come to the Balkans and there's an equivalent stream of Christians leaving the Balkans and settling in Constantinople, western Asia Minor and Pontus.
The Ottoman Empire doesn't fall due to involving itself in an unwinnable war but due to mass labor unrest. It shouldn't be too hard to have someone (maybe an Alevi or Sufi) appear that combines Islam with the ideals of Karl Marx. This Islamic socialist movement successfully pivots to both the laborers demanding better working conditions and the choice to organize and the ulema wanting more influence over the government. They take over most of the Ottoman Balkans and declare themselves the Islamic People's Republic of Rumelia, establishing their capital in Atina (Athens). The Ottoman sultan offers equal rights to the Christians but they don't bite: the sultan is deposed and the Christians declare the rebirth of the Roman Empire: crowning a Phanariote as Emperor of Rhomania. The Rhomanian government, with foreign backing, expands its control to most of Asia Minor and parts of Syria, using pogroms to wipe out anyone against the regime. The Arabs go their own way and form their own independent state led by the Hashemites who claim the Caliphate, disputed by the Rumelian ulema. Rumelia and Rhomania would have a population exchange later on, sending Muslims to the Rumelia and Christians to Rhomania.
