After the 1964 season, May was traded by the White Sox to the Philadelphia Phillies for catcher Bill Heath and a player to be named later (Joel Gibson).

May returned to the Major Leagues for good in 1969 with the Angels and appeared in 200 games between 1969 and the beginning of the 1974 season as a starter and reliever.

The Yankees traded May with Rick Dempsey, Scott McGregor, Tippy Martinez, and Dave Pagan to the Baltimore Orioles for Ken Holtzman, Doyle Alexander, Elrod Hendricks, Grant Jackson, and Jimmy Freeman at the trade deadline on June 15, 1976.

[9] He had fallen out of favor with Yankees manager Billy Martin over being removed prematurely from starts.

The Orioles traded May along with Randy Miller, and Bryn Smith to the Montreal Expos for Don Stanhouse, Joe Kerrigan and Gary Roenicke at the Winter Meetings on December 7, 1977.

During the 1980 season with New York, May led the American League with an earned run average of 2.46, which was his best career mark.

[13] Following his professional baseball career, May joined Circle K and worked as a store manager in California.