A team has finished a game with 11-17 singles and extra-base hits 1 time since 1897, most recently Boston Red Sox on 8 June 1950. That is about one every 443,004 team-games.
Box score for the most recent one ↗
11-8 11-9 11-10 11-11 11-12 11-13 11-17 12-0 12-1 12-2 12-3 12-4 12-5
The whole distribution — Singles and Extra-Base Hits · All 18 shapes