If you speak two languages, you are said to be bilingual. A polyglot can speak up to to six languages. When you get much beyond six, the term is hyperglot.
So what do you call a guy who can handle 200 languages?
Such a guy was Sir John Bowring, an English economist and writer who served as the fourth Governor of Hong Kong. Bowring was reported as knowing at least 200 languages and to be able to carry on a conversation in at least 100 of them.