A team has finished a game with 15-8 singles and extra-base hits 27 times since 1897, most recently Toronto Blue Jays on 29 May 2017. That is about one every 16,407 team-games.
Box score for the most recent one ↗
15-2 15-3 15-4 15-5 15-6 15-7 15-8 15-9 15-10 15-11 15-12 15-13 16-0
The whole distribution — Singles and Extra-Base Hits · All 18 shapes