Brandon Marshall had the most games with 17+ receptions, with 2 games.

most career games with 17 receptions (including postseason)
Interpreted as:
most career games by a player with 17 or more receptions (including postseason)
MarshallBrownWittenOwensGaines21111
NAMEGPRECTRGREC YDSAVGREC YDS/GREC TDRUSH YDSATTYPCRUSH YDS/GRUSH TD
Brandon MarshallBrandon Marshall239483669.4183.03000.00
Antonio BrownAntonio Brown1172328416.7284.0022211.022.00
Jason WittenJason Witten118231679.3167.00000.00
Terrell OwensTerrell Owens1202228314.2283.01515.05.00
Clark GainesClark Gaines1171609.4160.002054.020.00
StatMuse has game-level data for receptions going back to the 1960 season.