A team has finished a game with 15-11 singles and extra-base hits 4 times since 1897, most recently Baltimore Orioles on 16 August 2015. That is about one every 110,751 team-games.
Box score for the most recent one ↗
15-5 15-6 15-7 15-8 15-9 15-10 15-11 15-12 15-13 16-0 16-1 16-2 16-3
The whole distribution — Singles and Extra-Base Hits · All 18 shapes