On May 20, 1999 — Robin Ventura becomes the first major leaguer to hit grand slams in both games of a doubleheader, leading the New York Mets to a sweep over the Milwaukee Brewers, 11 – 10 and 10 – 1. On September 4, 1995, Ventura also hit two grand slams in a single game while playing for the Chicago White Sox.

Source:
Baseball Reference May 20