6 players were tied for the most games with 7+ intercepted passes, with 1 game. The first three are Ty Detmer, Steve DeBerg and Ken Stabler.

nfl most games with 7 passes intercepted player
Interpreted as:
NFL most regular-season games with 7 or more passes intercepted player
DetmerDeBergStablerWadeBratkowskiHardy111111
NAMEGPINTCMPATTPCTYDSAVGYDS/GTDTD%INT%SCKSCKYRATE
Ty DetmerTy Detmer17224252.42125.0212.012.416.732335.1
Steve DeBergSteve DeBerg17184045.02145.4214.012.517.531930.6
Ken StablerKen Stabler17204050.02746.9274.012.517.541.0
Tommy WadeTommy Wade17223857.92787.3278.012.618.450.0
Zeke BratkowskiZeke Bratkowski17122842.91786.4178.013.625.036.6
Jim HardyJim Hardy18123930.81934.9193.012.620.517.3
StatMuse has game-level data for intercepted passes going back to the 1950 season.

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