Jared Goff had the most games by a Rams quarterback with 400+ passing yards and 4+ passing touchdowns, with 2 games.

which rams qb has the most career games with 400 passing yards and 4 tds
Interpreted as:
Which rams qb has the most career regular-season games with 400 or more passing yards and 4 or more passing tds?
GoffBulgerVan Brocklin211
NAMEGPYDSTDCMPATTPCTAVGYDS/GTD%INTINT%SCKSCKYRATE
Jared GoffJared Goff28789578269.510.7439.011.000.0643141.2
Marc BulgerMarc Bulger14534364875.09.4453.08.300.000131.7
Norm Van BrocklinNorm Van Brocklin15545274165.913.5554.012.224.9128.3
StatMuse has game-level data for passing touchdowns and passing yards going back to the 1950 season.

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