A team has finished a game with 16-11 singles and extra-base hits 3 times since 1897, most recently Texas Rangers on 25 July 2011. That is about one every 147,668 team-games.
Box score for the most recent one ↗
16-5 16-6 16-7 16-8 16-9 16-10 16-11 16-12 17-0 17-1 17-2 17-3 17-4
The whole distribution — Singles and Extra-Base Hits · All 18 shapes