Jerry Rice had the most games with 3+ receiving touchdowns, with 11 games.

who has the most 3 touchdown receiving games
Interpreted as:
Who has the most 3 or more touchdown receiving regular-season games?
RiceMossHarrisonRandleOwensWalkerPickensWinslowShofnerMcDonaldBaldwinGronkowskiGatesJohnsonMossRobinsonBruceCarterFryarSharpeSharpeRison11996554444333333333333
NAMEGPREC TDRECTRGREC YDSREC AVGREC YDS/GRUSH YDSATTRUSH AVGRUSH YDS/GRUSH TD
Jerry RiceJerry Rice113697101,77718.3161.53548.83.20
Randy MossRandy Moss92866731,20718.3134.11728.51.90
Marvin HarrisonMarvin Harrison92773841,10615.2122.9000.00
Sonny RandleSonny Randle6184586719.3144.5000.00
Terrell OwensTerrell Owens516365060316.8120.6616.01.20
Wesley WalkerWesley Walker5162972525.0145.0000.00
Carl PickensCarl Pickens4123859015.5147.5000.00
Kellen WinslowKellen Winslow4144253312.7133.3000.00
Del ShofnerDel Shofner4122150023.8125.0414.01.00
Tommy McDonaldTommy McDonald4122363427.6158.5000.00
Doug BaldwinDoug Baldwin39182528615.995.3000.00
Rob GronkowskiRob Gronkowski39192231516.6105.0000.00
Antonio GatesAntonio Gates39223229713.599.0000.00
Chad JohnsonChad Johnson39284140014.3133.3313.01.00
Santana MossSantana Moss39192941922.1139.71125.53.70
Marcus RobinsonMarcus Robinson310212933315.9111.0000.00
Isaac BruceIsaac Bruce310202738319.2127.7000.00
Cris CarterCris Carter39211231114.8103.7000.00
Irving FryarIrving Fryar3102345119.6150.3000.00
Shannon SharpeShannon Sharpe39301231910.6106.3000.00
Sterling SharpeSterling Sharpe3112840114.3133.7723.52.30
Andre RisonAndre Rison392333714.7112.3000.00
Steve LargentSteve Largent392746717.3155.7000.00
Todd ChristensenTodd Christensen392637414.4124.7000.00
Leonard ThompsonLeonard Thompson391930616.1102.0-131-13.0-4.30
StatMuse has game-level data for receiving touchdowns going back to the 1960 season.

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