The Denver Broncos have the most games by a team with 4+ passing touchdowns in a season, with 9 games in 2013.

which nfl an has the most 4 td passing games in a season
Interpreted as:
Which NFL an has the most 4 or more td passing games in a season?
2013Broncos2020Packers2018Chiefs1961Oilers2011Packers2004Colts1998Vikings1986Dolphins1984Dolphins2020Bills2020Seahawks2018Buccaneers2017Eagles2013Saints2011Saints2007Patriots2004Eagles1996Packers1950Rams2020Buccaneers2019Ravens2016Packers2016Saints97776666655555555554444
TEAMSEASONGPTDCMPATTPCTYDSAVGYDS/GTD%INTINT%SCKSCKYRATE
Denver BroncosDenver Broncos201394027238770.33,4488.9383.110.361.61275125.8
Green Bay PackersGreen Bay Packers202072816822076.41,9618.9280.112.710.5443140.5
Kansas City ChiefsKansas City Chiefs201873216924868.12,3689.5338.312.972.8951126.5
Houston OilersHouston Oilers196173112623553.62,54310.8363.313.2104.3229113.7
Green Bay PackersGreen Bay Packers201162715521771.42,0759.6345.812.441.81570133.4
Indianapolis ColtsIndianapolis Colts200462913519967.81,9079.6317.814.642.0212129.8
Minnesota VikingsMinnesota Vikings199862410918558.91,85810.0309.713.031.6638125.9
Miami DolphinsMiami Dolphins198662716826064.62,1238.2353.810.451.91064116.6
Miami DolphinsMiami Dolphins198462515123763.72,0338.6338.810.573.0774113.8
Buffalo BillsBuffalo Bills202052013418672.01,8339.9366.610.831.6759132.3
Seattle SeahawksSeattle Seahawks202052213117276.21,4258.3285.012.821.21271134.8
Tampa Bay BuccaneersTampa Bay Buccaneers201852012417869.71,80210.1360.411.263.4843125.7
Philadelphia EaglesPhiladelphia Eagles201752010717262.21,3768.0275.211.631.7964118.8
New Orleans SaintsNew Orleans Saints201352114418777.01,8319.8366.211.200.01068144.5
New Orleans SaintsNew Orleans Saints201152314219274.01,8259.5365.012.031.6312136.4
New England PatriotsNew England Patriots200752414119074.21,8509.7370.012.610.5528141.9
Philadelphia EaglesPhiladelphia Eagles200452111917866.91,7379.8347.411.821.11364133.1
Green Bay PackersGreen Bay Packers199652010416363.81,2927.9258.412.342.51050117.6
Los Angeles RamsLos Angeles Rams195052410517958.71,7559.8351.013.495.0546110.5
Tampa Bay BuccaneersTampa Bay Buccaneers202041912017469.01,6289.4407.010.921.1322130.1
Baltimore RavensBaltimore Ravens20194207410074.01,03410.3258.520.000.0514146.4
Green Bay PackersGreen Bay Packers20164169814070.01,0987.8274.511.400.01071131.2
New Orleans SaintsNew Orleans Saints201641712817672.71,6379.3409.39.710.6754131.3
Washington RedskinsWashington Redskins20154169212573.61,31210.5328.012.800.0761146.7
Denver BroncosDenver Broncos201441711415872.21,4078.9351.810.842.5425124.6
Indianapolis ColtsIndianapolis Colts201441710615767.51,5079.6376.810.821.3423129.1
New Orleans SaintsNew Orleans Saints201241611116467.71,4508.8362.59.831.8646120.2
Green Bay PackersGreen Bay Packers20124189714865.51,2408.4310.012.221.4852125.6
Detroit LionsDetroit Lions201141811718762.61,5688.4392.09.652.7643110.1
Indianapolis ColtsIndianapolis Colts20094169515162.91,2348.2308.510.674.6111104.6
Dallas CowboysDallas Cowboys20074167611466.71,19410.5298.514.043.5319126.2
Minnesota VikingsMinnesota Vikings200441910715668.61,4639.4365.812.221.31134132.6
StatMuse has team, game-level data for passing touchdowns going back to the 1940 season.

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