A team has finished a game with 6-11 singles and extra-base hits 24 times since 1897, most recently Cincinnati Reds on 29 September 2023. That is about one every 18,458 team-games.
Box score for the most recent one ↗
5-17 6-6 6-7 6-8 6-9 6-10 6-11 6-12 6-13 6-14 7-5 7-6 7-7
The whole distribution — Singles and Extra-Base Hits · All 18 shapes