A team has finished a game with 8-12 singles and extra-base hits 4 times since 1897, most recently Toronto Blue Jays on 7 August 2010. That is about one every 110,751 team-games.
Box score for the most recent one ↗
8-6 8-7 8-8 8-9 8-10 8-11 8-12 8-13 8-14 9-3 9-4 9-5 9-6
The whole distribution — Singles and Extra-Base Hits · All 18 shapes