A team has finished a game with 19-10 singles and extra-base hits 2 times since 1897, most recently Toronto Blue Jays on 22 July 2022. That is about one every 221,502 team-games.
Box score for the most recent one ↗
19-4 19-5 19-6 19-7 19-8 19-9 19-10 19-11 20-0 20-1 20-2 20-3 20-4
The whole distribution — Singles and Extra-Base Hits · All 18 shapes