A team has finished a game with 3-11 singles and extra-base hits 8 times since 1897, most recently Tampa Bay Rays on 7 September 2021. That is about one every 55,375 team-games.
Box score for the most recent one ↗
2-10 2-11 2-12 2-13 3-9 3-10 3-11 3-12 3-13 4-8 4-9 4-10 4-11
The whole distribution — Singles and Extra-Base Hits · All 18 shapes