Josh Devore of the New York Giants stole 4 bases in the 9th inning of a game against Boston that ended 21-12 in favor of New York, with 17 of those runs (7 by NY, 10 by Boston) coming in the 9th inning alone. Not sure how many of the 4000 attendees stuck around for the final frantic frame, given the visiting Giants' 14-2 lead after 8. (Box score:
https://www.baseball-reference.com/b...91206200.shtml)
Devore entered as a sub for RF Beals Becker, reached base on 3-of-4 PAs, and stole 2nd and 3rd twice in the 9th off pitcher Brad Hogg, who Boston left in for the last six innings to absorb 12 of NY's 21 runs. For their part, the Giants put 21yo Ernie Shore on the mound in the ninth for his major league debut to hold the 21-2 lead. He finished that one inning, gave up 10 runs, "earned a save," and didn't pitch again until two years later.
SABR's bio notes that some historians later disputed Devore's four steals as described at the time. It's quite possible infielders didn't try to hold men on base, given the Giants lop-sided lead. Either way, no one since stole more than four.