In early 1968, Moore’s band traveled to Europe and Moye decided to live there for the next couple of years, touring and visiting the continent as well as Northern Africa.

By 1969, the AEC had become a quartet of Roscoe Mitchell, Joseph Jarman (saxophones), Lester Bowie (trumpet) and Malachi Favors Maghostut (bass), with no full-time drummer though all the musicians doubled on various percussion instruments.

Moye at the time was rehearsing and performing in Paris, France, at the American Center for Students and Artists, where musicians such as Art Taylor and Johnny Griffin practiced collectively.

In the mid-1980s, Moye joined The Leaders, a jazz group consisting of AEC member Bowie, Chico Freeman, Arthur Blythe, Cecil McBee, and Kirk Lightsey.

"[5] With the Art Ensemble of Chicago With The Leaders With Hamiet Bluiett With Kenny Clarke, Andrew Cyrille, and Milford Graves With Chico Freeman With Julius Hemphill With Joseph Jarman With Oliver Lake With Cecil McBee With Marcello Melis With Don Pullen With Alan Silva With Sirone With Wadada Leo Smith With Randy Weston