A team has finished a game with 17-4 singles and extra-base hits 64 times since 1897, most recently Boston Red Sox on 15 September 2017. That is about one every 6,921 team-games.
Box score for the most recent one ↗
16-11 16-12 17-0 17-1 17-2 17-3 17-4 17-5 17-6 17-7 17-8 17-9 17-10
The whole distribution — Singles and Extra-Base Hits · All 18 shapes