Yes.
1) 1904 Boston Americans (now Red Sox): Cy Young threw a perfect game and Jesse Tannehill threw a no-hitter.
2) 1908 Cleveland Naps (now Indians): Addie Joss threw a perfect game and Bob Rhoads threw a no-hitter.
3) 2010 Philadelphia Phillies: Roy Halladay threw both a perfect game and no-hitter. The no-hitter came in the playoffs.
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Los Angeles Angels
Rangers, twins
Chicago Cubs
There are 162 games in a MLB regular season. Add that to as many as 36 exhibition games and a possible 19 post season games and MLB team could play as many as 217 games in a year.
The MLB record for fewest wins by a team in a season was set by the 1899 Cleveland Spiders. They won 20 games that season and lost 134. The 134 losses is also an MLB record for most losses by a team in a season.