A team has finished a game with 11-11 singles and extra-base hits 10 times since 1897, most recently Atlanta Braves on 12 August 2023. That is about one every 44,300 team-games.
Box score for the most recent one ↗
11-5 11-6 11-7 11-8 11-9 11-10 11-11 11-12 11-13 11-17 12-0 12-1 12-2
The whole distribution — Singles and Extra-Base Hits · All 18 shapes