He was also a member of progressive rock band National Health and jazz-rock supergroup Soft Heap, and has recorded several solo albums, including Accident (1982), Parrot Fashions (1984), The Caretaker (2001) and Greaves Verlaine (2008).

Greaves had met and worked with Blegvad during the brief merger of Henry Cow and Slapp Happy between November 1974 and April 1975, their first collaboration, "Bad Alchemy", appearing on the two bands' joint album Desperate Straights.

He toured with the band, appearing on the album Of Queues and Cures, for which he wrote the instrumental tour-de-force "Squarer for Maud", the later reunion effort DS Al Coda (1982) and the archive release Play Time.

For his next album, 1991's La Petite Bouteille de Linge (Little Bottle of Laundry), Greaves retained the services of Ovide on guitar, adding his old mate Pip Pyle on drums and the latter's then-partner, Sophia Domancich on piano.

He also played bass in Blegvad's own trio alongside Chris Cutler on drums, which recorded two studio albums, later expanding into a quintet with Bob Drake on guitar and Karen Mantler on organ.

He contributed lyrics and vocals to two songs on saxophonist Julien Lourau's acclaimed Fire & Forget (2005), to much of Sophia Domancich's Snakes & Ladders (2010) sharing the microphone with Himiko Paganotti and Robert Wyatt, and sang all the vocals on Alain Blésing's Songs From The Beginning project, revisiting 1970s progressive rock classics by King Crimson, Soft Machine, Henry Cow and Hatfield and the North among others, Catherine Delaunay's Sois Patient Car Le Loup (2011), the French clarinettist's settings of texts by Malcolm Lowry, and Post Image's In an English Garden (2012), a special project celebrating the jazz-fusion group's 25th anniversary.

In addition to his Roxongs bandmates, the album featured regular collaborators Jeanne Added (vocals) and Scott Taylor (accordion, trumpet), as well as appearances by Karen Mantler and Dominique Pifarély.

In 2012, Greaves embarked on yet another Verlaine project, this time composing to an original libretto by Emmanuel Tugny and teaming up with a trio of French vocalists, Elise Caron, Jeanne Added and Thomas de Pourquery.

Another improvising unit including fellow Henry Cow alumni was The Artaud Beats, formed in 2009 and consisting of Greaves, Cutler, Geoff Leigh and Yumi Hara.

Greaves recites texts (mostly by Cutler) over variations on Henry Cow and Art Bears music re-interpreted by a jazz quintet which includes former collaborators Sophia Domancich, Sylvain Kassap and Simon Goubert.

He has partnered with Barbazza for duo gigs, as documented on the live album Earthly Powers, which includes covers of Bob Dylan and Leonard Cohen and a new song each by the performers.

Greaves has performed (bass and occasional vocals) in Folly Bololey, a reinterpretation of Robert Wyatt's Rock Bottom by the North Sea Radio Orchestra, premiered in 2014 at the Nuits de Fourvière festival, with Annie Barbazza as principal vocalist and other guests including William D. Drake (Cardiacs).

In it, Greaves set texts by Guillaume Apollinaire, alongside fellow vocalists Jeanne Added and Himiko Paganotti, with guitarist Olivier Mellano, another regular collaborator, in the co-producer's chair.

Greaves, Mellano and drummer Régis Boulard also perform as a rock trio under the name Gloyw, playing both improvised and composed music with texts, with an album due for release in May 2024.

On August 5th 2023, Greaves and Friends, featuring Jakko Jakszyk and the latter's King Crimson bandmate Mel Collins, along with Barbazza, Valero and Boulard, played a one-off concert in Piacenza.

With Henry Cow With The Lodge With National Health With Pip Pyle and Philippe Marcel Iung With The Artaud Beats With Peter Blegvad With Catherine Delaunay With Sophia Domancich With Michel Edelin Quintet [fr] With Julien Lourau With Michael Mantler With the North Sea Radio Orchestra With Michael Nyman Band With Pip Pyle With Post Image With Silvain Vanot With Robert Wyatt With Annie Barbazza [it]