All Turkiye may need from Egypt is for them to agree to remain neutral in any conflict between Greece and Turkiye. Egypt may agree to co-operate in this manner if Turkiye eliminates possible threats on Egypts borders, helps maintain peace, and agrees to not encroach upon Egyptian interests...
The four countries Turkiye may have to control to gain full superiority over the eastern Mediterranean are Greece, Libya, Israel, and Cyprus. If Egypt co-operates with Turkiye against Greece then the Turks could annex the island of Crete and maintain pressure on but not invade the rest of Greek...