A team has finished a game with 15-10 singles and extra-base hits 6 times since 1897, most recently Minnesota Twins on 4 June 2002. That is about one every 73,834 team-games.
Box score for the most recent one ↗
15-4 15-5 15-6 15-7 15-8 15-9 15-10 15-11 15-12 15-13 16-0 16-1 16-2
The whole distribution — Singles and Extra-Base Hits · All 18 shapes