A team has finished a game with 20-10 singles and extra-base hits 1 time since 1897, most recently New York Yankees on 28 September 1923. That is about one every 443,004 team-games.
Box score for the most recent one ↗
20-4 20-5 20-6 20-7 20-8 20-9 20-10 21-0 21-1 21-2 21-3 21-4 21-5
The whole distribution — Singles and Extra-Base Hits · All 18 shapes