A team has finished a game with 11-12 singles and extra-base hits 3 times since 1897, most recently Pittsburgh Pirates on 1 July 2019. That is about one every 147,668 team-games.
Box score for the most recent one ↗
11-6 11-7 11-8 11-9 11-10 11-11 11-12 11-13 11-17 12-0 12-1 12-2 12-3
The whole distribution — Singles and Extra-Base Hits · All 18 shapes