Not like this. Correct solution: "Én sem Kati vagyok"

"Nem Kati vagyok én sem" well, it's grammatically good but it's rather strange...I wouldn't use it..It's too strained.

Not correct. The word sem needs the word én which it is negating to appear with it.

Well, sorry, I suppose you could say Kati sem vagyok - as in, (I'm not Zsuzsa and) I'm not Kati either. But Sem at the beginning of the sentence like you have it wouldn't really work.