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Drew Brees had the most games with 300+ passing yards and 3+ passing touchdowns, with 67 games.

who has the most career games with at least 300 passing yards and 3 passing touchdowns
Interpreted as:
Who has the most career regular-season games with at least 300 passing yards and 3 or more passing touchdowns?
BreesBradyManningRodgersMarinoRoethlisbergerRiversCousinsStaffordMahomesFavreWarnerRyanRomoMontanaFoutsGoffPrescottManningYoungJurgensenBurrow67654640333230292927272322222120191919181817
NAMEGPYDSTDCMPATTPCTAVGYDS/GINTRTGTD%INT%SCKSCKY
Drew BreesDrew Brees6724,4702451,9302,69271.79.1365.238124.29.11.487586
Tom BradyTom Brady6523,5872331,8162,60969.69.0362.937121.68.91.499617
Peyton ManningPeyton Manning4616,7271701,2691,79070.99.3363.636123.49.52.037236
Aaron RodgersAaron Rodgers4013,8231461,0431,51169.09.1345.69127.59.70.688625
Dan MarinoDan Marino3312,2421228681,39462.38.8371.048105.48.83.435288
Ben RoethlisbergerBen Roethlisberger3211,7511139331,34669.38.7367.219118.38.41.461401
Philip RiversPhilip Rivers3010,537947981,15569.19.1351.231113.68.12.743246
Kirk CousinsKirk Cousins2910,537968411,17271.89.0363.314121.78.21.263473
Matthew StaffordMatthew Stafford2910,314997781,18665.68.7355.722113.18.31.960430
Patrick MahomesPatrick Mahomes2710,1451017611,06571.59.5375.717126.39.51.629166
Brett FavreBrett Favre279,365917371,09567.38.6346.921113.58.31.936245
Kurt WarnerKurt Warner237,8257655179969.09.8340.224119.59.53.048295
Matt RyanMatt Ryan228,0727663790470.58.9366.912120.58.41.345301
Tony RomoTony Romo227,6717454780667.99.5348.719119.19.22.434238
Joe MontanaJoe Montana217,6667354980568.29.5365.020118.59.12.537250
Dan FoutsDan Fouts207,4326951181262.99.2371.629106.18.53.6
Jared GoffJared Goff196,8696651674269.59.3361.57124.38.90.928212
Dak PrescottDak Prescott197,2386555679370.19.1380.912119.68.21.538236
Eli ManningEli Manning197,1976554978869.79.1378.824113.08.23.032209
Steve YoungSteve Young186,4845942964766.310.0360.213121.19.12.025111
Sonny JurgensenSonny Jurgensen186,5646540667760.09.7364.731105.49.64.6
Joe BurrowJoe Burrow176,5275754576171.68.6383.910117.07.51.352344
Carson PalmerCarson Palmer175,9665745668766.48.7350.919109.78.32.836275
Andrew LuckAndrew Luck165,8305845072362.28.1364.417104.58.02.428195
Boomer EsiasonBoomer Esiason165,9535339663062.99.4372.120108.78.43.232237
Johnny UnitasJohnny Unitas
Josh AllenJosh Allen
Russell WilsonRussell Wilson
Joe FlaccoJoe Flacco
Andy DaltonAndy Dalton
Warren MoonWarren Moon
Jameis WinstonJameis Winston
Ryan FitzpatrickRyan Fitzpatrick
Donovan McNabbDonovan McNabb
Drew BledsoeDrew Bledsoe
Jim KellyJim Kelly
Trent GreenTrent Green
John ElwayJohn Elway
Brian SipeBrian Sipe
George BlandaGeorge Blanda
Justin HerbertJustin Herbert
Derek CarrDerek Carr
Kerry CollinsKerry Collins
Rich GannonRich Gannon
Jim EverettJim Everett
Y.A. TittleY.A. Tittle
Matt SchaubMatt Schaub
Daunte CulpepperDaunte Culpepper
Vinny TestaverdeVinny Testaverde
Baker MayfieldBaker Mayfield
StatMuse has game-level data for passing touchdowns and passing yards going back to the 1950 season.

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