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A party system is a concept in comparative political science concerning the system of government by political parties in a democratic country. The idea is that political parties have basic similarities: they control the government, have a stable base of mass popular support, and create internal mechanisms for controlling funding, information and nominations.
The concept was originated by European scholars studying the United States, especially James Bryce and Moisey Ostrogorsky, and has been expanded to cover other democracies. Giovanni Sartori devised the most widely used classification method for party systems. He suggested that party systems should be classified by the number of relevant parties and the degree of fragmentation.Party systems can be distinguished by the effective number of parties.

From Wiki.

Yes. We have Democrats here, as well as Republicans,  Independents, Liberals and I suspect, some communists as well.