A team has finished a game with 20-4 singles and extra-base hits 7 times since 1897, most recently Colorado Rockies on 3 May 2000. That is about one every 63,286 team-games.
Box score for the most recent one ↗
19-10 19-11 20-0 20-1 20-2 20-3 20-4 20-5 20-6 20-7 20-8 20-9 20-10
The whole distribution — Singles and Extra-Base Hits · All 18 shapes