In around 1700BC, the Hittites adapted Assyrian cuneiform (which was basically just Akkadian cuneiform which had been around long enough to evolve slightly) to their language. They only took about half of the symbols from Assyrian cuneiform, of which roughly half were syllables and half logograms.
Hittite used determinatives, all of which were Sumerian logograms that the Akkadians/Assyrians had incorporated into their own writing. Yes, 1500 years after the development of Sumerian cuneiform, after three different changes in language (Sumerian->Akkadian->Assyrian->Hittite), the Sumerian maintained a recognizable identity.
One interesting thing about Hittite cuneiform is that there were words that the Hittites borrowed from Assyrian which the Assyrians spelled phonetically, but which the Hittites used as logograms.