Here's what I found at Retrosheet.org about getting two stolen bases on the same pitch, but I think Phillips takes the honors for the purity of his play.
6-10-1911 BRO @ PIT - The Pirates' Bobby Byrne stole around the horn in an unusual fashion. His trip began as part of a double steal with Fred Clarke on 3b. Clarke scored on a controversial call, and while Dodgers' catcher Bill Bergen jawed at plate umpire Bill Klem, Byrne snuck to 3b and apparently was awarded a stolen base. Dots Miller walked, and the double steal was worked again, completing Byrne's circuit. It was an unusual game for baserunning: the Pirates suffered a 64(1)4(2)/DP when pitcher Babe Adams running on 2b for some reason attempted to scamper back to second on a ground ball (perhaps forgetting the force?), and the Pirates attempted a triple steal in the eighth up 8-0, which succeeded in scoring a run but only due to a throwing error (no stolen bases were awarded).
6/19/71: In the top of the 14th at Shea Stadium, Larry Bowa was on 2b and Oscar Gamble on 1b for the Phillies. On a double steal attempt, Bowa reaches 3b and Gamble is caught in a rundown. Bowa continues on to score and draws a throw while Gamble reaches 2b. NL president Chub Feeney ruled that Bowa should be credited with 2 stolen bases on the play and Gamble 1.