A team has finished a game with 20-3 singles and extra-base hits 14 times since 1897, most recently Chicago White Sox on 25 June 2002. That is about one every 31,643 team-games.
Box score for the most recent one ↗
19-9 19-10 19-11 20-0 20-1 20-2 20-3 20-4 20-5 20-6 20-7 20-8 20-9
The whole distribution — Singles and Extra-Base Hits · All 18 shapes