I had a sneaking suspicion that K was Sigma (or somehow closely related) but I never had a good reasoning behind it.
I think it was the whole getting woozy part on the left most path, when Sigma and Phi were in the surveilence room or whatever. He feel asleep for seemingly no reason, and then shortly after that K and Dio were found dead. That combined with Sigma also feeling woozy right before killing himself in the clover ending, Ks body being nowhere found in the piles of our dead friends. It was an outlandish theory for sure. But there must have been some reason why we never see Ks face.
Cool ending! Now I got the Username for the directors office, just gotta find the password.