A system in which more than two political parties contest for an election is referred to as

A multi-party system is a political system in which more than two political parties have a realistic chance of contesting and winning elections, either independently or as part of a coalition. In such a system, multiple parties compete for political power, and no single party is guaranteed dominance.

Nigeria operates a multi-party system. Since the return to democracy in 1999, Nigeria has had numerous registered political parties contesting elections at various levels - federal, state, and local government.

The other options describe different party systems. A one-party system is one in which only a single political party is legally permitted to hold power (as in some authoritarian states). A two-party system is one in which only two major parties dominate the political landscape (such as the United States with the Democrats and Republicans). A zero-party system is not a recognised classification in standard political science - every political system has at least the concept of organised political participation.

The key feature that defines a multi-party system is the presence of more than two viable political parties competing in elections, which is exactly what the question describes.