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Though unsure how doable it is the challenge is to have the Byzantines manage to successfully Hellenize most of the South Slavic and Turkic peoples within the Balkans and Anatolia respectively.
The Hellenization can either be total or largely successful, with the latter scenario at least allowing for the remaining non-Hellenized Slavic and Turkic populations in the Balkans and Anatolia to eventually form their own polities.