Polyglotism is the ability to speak several languages with a high degree of proficiency. There is no consensus on exactly how many languages a person has to speak to be a polyglot. One could say "four or more", since speakers of two or three languages are commonly called bilingual and trilingual, respectively. The term multilingual is similar.
Linguist Richard Hudson uses the term "hyperpolyglot" for a person who can speak six or more languages fluently.