Jerry Rice has the most catches in a game with 3+ receiving touchdowns, with 16 receptions against the Rams on November 20, 1994.

what are the most receptions by a player in a game with at least three touchdowns
Interpreted as:
What are the most receptions by a player in a regular-season game with at least three receiving touchdowns?
Results may be incomplete. StatMuse has complete game-level data for receiving touchdowns and receptions going back to the 1960 season.