A team has finished a game with 2-12 singles and extra-base hits 2 times since 1897, most recently Montreal Expos on 21 August 2002. That is about one every 221,502 team-games.
Box score for the most recent one ↗
1-11 2-10 2-11 2-12 2-13 3-9 3-10 3-11 3-12 3-13
The whole distribution — Singles and Extra-Base Hits · All 18 shapes