This is a party system whereby more than two parties are constitutionally recognized. Nigeria is a good example of a country practising a multi-party system. In the first republic, Nigeria had about three to five parties, and in the second Republic.
She had about six parties while in the Third Republic, about three parties were floated.
Today, Nigeria has about thirty political parties currently in existence, Other examples of countries practising a multiparty system are France, Italy, India, Germany etc.