A team has finished a game with 8-14 singles and extra-base hits 4 times since 1897, most recently Boston Red Sox on 26 September 2018. That is about one every 110,751 team-games.
Box score for the most recent one ↗
8-8 8-9 8-10 8-11 8-12 8-13 8-14 9-3 9-4 9-5 9-6 9-7 9-8
The whole distribution — Singles and Extra-Base Hits · All 18 shapes