Originally meant only to play a single date at a festival in Clusone, Italy, the trio toured irregularly for several years and recorded six albums, including one of freely-interpreted Irving Berlin compositions.

Moore also plays in Jewels and Binoculars, a collective trio with bassist Lindsey Horner and drummer Michael Vatcher which is devoted to interpretations of Bob Dylan songs.

Moore started his jazz quintet in 2005, in which he works with accomplished Dutch players: trumpeter Eric Vloeimans, pianist Marc van Roon, bassist Paul Berner, and drummer Owen Hart, Jr.

In 2013, he performed with InstanPool, a group of international musicians making improved music and occasionally playing a composition.

InstanPool consists of Michael Moore and Mark Alban Lotz (winds), Korhan Erel and Robert van Heumen (laptops), Sevket Akinci and Giray Gürkal (guitars, electronics).