On this page are galleries of the costumes able to be validated (either as primarily or secondarily) in one or more other detachments of the Rebel Legion than the Galactic Senate. This is not an exhaustive list as there are many more potential dual-detachment costumes that do not yet have galleries.
All the cross-detachment costumes
As a Rebel Legion member with a relevant costume, you can apply here to join the RLGS detachment.
Clones of the Republic
Docking Bay 94
Galactic Strategic Command
Knights of the Jedi Order
United Citizens of the Galactic Republic