From June 1906 to June 1907 the Cubs had a .799 winning pct

From June 1906 to June 1907 the Cubs were 123-31 in regular season games, a .799 pct, much higher than anyone else for 154 games (I actually did 157 games because they had 3 ties). The 1905-06 Cubs have some spans next, but that is pretty much the same team.

https://stathead.com/tiny/yfUYd

The next different team to come in is the Cardinals in 1943-44 at .760. You might not be able to see that because you have to go to the next page at Stathead and to do that you might have to be a subscriber.

Then the 1927-28 Yankees have a .758 span. Then the Pirates 1908-09 have .756 and the Pirates 1901-02 had a .753 span.

Those are all the teams with .750 or higher.