As the band developed their repertoire into the 21st century, they turned their attention to Ethiojazz and were backing Addis Ababa saxophonist Getachew Mekurya on world tours and for his 2006 album Moa Anbessa with French, Dutch, and Canadian musicians Xavier Charles, Joost Buis, and Brodie West on clarinet, trombone and alto saxophone.

Amidst these collaborations with The Ex, a new international collective of horn players gradually formed and by 2010 adopted the name "Brass Unbound" after Johan van der Keuken's 1993 film of the same name.

[5] A popular love song by Ethiopian singer Mahmoud Ahmed that had long been in The Ex's live set with Getatchew Mekurya is sung by drummer Katherina Bornefeld.

[5] Previously unreleased songs comprise the remainder of the album, leading with the North African-inspired "Last Famous Words", with others exploring themes from punk culture, free jazz, and leftist politics.

[10] Pitchfork's Douglass Wolk called Enormous Door "an acrobatic, ferocious record, a welcome burst of electric noise and squealing horns from a group whose power and flexibility keep growing with time.