Dear Rhadamantys,
I think Egyptians were more "consolidated" than Hittites - we know at least 3 indoeuropean (Hittite, Luwian and Palaian), Hurrian and "Hattili" languages spoken in Hittite empire. It seems the situatiom looks like in Britain in Edward I times - french-spoken nobility, saxon majority, celtic Walles and Highland.
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Maybe Hittite king adopted Egyptian "I"? In any case, diplomacy had been developed, kings tried to form some hierarchy and equivalent rulers named themselves similar in documents. We know that Hittite tabarna (great king) thought he was equal to Pharao, king of Babylon, king of Assyria and king of Ahhiawa (Mykenian Greece?).