A team has finished a game with 14-11 singles and extra-base hits 6 times since 1897, most recently New York Mets on 16 August 2018. That is about one every 73,834 team-games.
Box score for the most recent one ↗
14-5 14-6 14-7 14-8 14-9 14-10 14-11 14-12 14-13 14-14 15-0 15-1 15-2
The whole distribution — Singles and Extra-Base Hits · All 18 shapes