Now why would you need Elias Sports Bureau when you've got me?
In answer to your question, the 1936 Yankees of Lou Gehrig and rookie Joe DiMaggio and five 100 RBI men scored ten or more runs 41 times. The 1930 NY Yankees of Babe Ruth and Lou Gehrig did the feat 36 times and 33 more times in 1931. In the latter 1920's through 1930's it was not uncommon for multiple teams to score ten or more runs 26-30 times.
The Boston Red Sox of 1950, even with Ted Williams limited to less than 90 games by injury scored over 1000 runs and scored ten or more 34 times and 27 times in 1949, the year before. They were led by Vern Stephens 144 and 159 RBI's in those two seasons, as well as rookie Walt Dropo with 144 RBI's in only 136 games in 1950, along with Williams, Dominic DiMaggio and Bobby Doerr.
For a modern comparison, the 1999 Cleveland Indians scored 1009 runs and scored ten or more runs 28 times.
Along the same line, the worst pitching team of all time, the 1930 Philadelphia Phillies scored 944 runs and hit .315 as a team. Unfortunately, they gave up 1199 runs scored and allowed ten or more runs an incredible 45 times. They naturally finished in last place!
The team many consider the greatest of all time, the 1927 Yankees scored ten or more runs "only" 26 times.
