In the early 2000s, there was an experiment to see if companies could be listed on two major (i.e. competing) exchanges simultaneously. Ultimately, the trend didn't catch on and the program was ended. Since then, 1 stock = 1 exchange (at least in the U.S.).
Note: Exchange ≠ Market (i.e. trading venue).
Every exchange is a market, but not all markets are stock exchanges.
Sources: Hegde, Lin and Varshney (2010) [2140]; Hegde, Lin and Varshney (2017) [2141]
Fun Fact: IEX also experimented with starting its own national market, but was only able to sign up Interactive Brokers. BATS, however, was more slightly successful at getting listings: it snagged its parent company CBOE (the rest are just ETFs).