A team has finished a game with 7-12 singles and extra-base hits 9 times since 1897, most recently Boston Red Sox on 4 September 2013. That is about one every 49,222 team-games.
Box score for the most recent one ↗
7-6 7-7 7-8 7-9 7-10 7-11 7-12 7-13 7-14 7-15 8-4 8-5 8-6
The whole distribution — Singles and Extra-Base Hits · All 18 shapes