A team has finished a game with 16-3 singles and extra-base hits 144 times since 1897, most recently Toronto Blue Jays on 30 March 2023. That is about one every 3,076 team-games.
Box score for the most recent one ↗
15-11 15-12 15-13 16-0 16-1 16-2 16-3 16-4 16-5 16-6 16-7 16-8 16-9
The whole distribution — Singles and Extra-Base Hits · All 18 shapes