A team has finished a game with 12-11 singles and extra-base hits 8 times since 1897, most recently Washington Nationals on 30 April 2017. That is about one every 55,375 team-games.
Box score for the most recent one ↗
12-5 12-6 12-7 12-8 12-9 12-10 12-11 12-12 12-13 13-0 13-1 13-2 13-3
The whole distribution — Singles and Extra-Base Hits · All 18 shapes