A team has finished a game with 16-4 singles and extra-base hits 107 times since 1897, most recently Chicago Cubs on 17 April 2023. That is about one every 4,140 team-games.
Box score for the most recent one ↗
15-12 15-13 16-0 16-1 16-2 16-3 16-4 16-5 16-6 16-7 16-8 16-9 16-10
The whole distribution — Singles and Extra-Base Hits · All 18 shapes