A team has finished a game with 7-15 singles and extra-base hits 1 time since 1897, most recently Cleveland Guardians on 13 July 1996. That is about one every 443,004 team-games.
Box score for the most recent one ↗
7-9 7-10 7-11 7-12 7-13 7-14 7-15 8-4 8-5 8-6 8-7 8-8 8-9
The whole distribution — Singles and Extra-Base Hits · All 18 shapes