It is not known if there are any others; Branko Grünbaum conjectured that there are not, but thought that a proof would be "probably quite complicated".
They can both be constructed from a uniform polyhedron by twisting one cupola-shaped cap.
As the name suggests, it can be constructed by elongating a square gyrobicupola (J29) and inserting an octagonal prism between its two halves.
The construction of the uniform and pseudo rhombicuboctahedra can be seen in the following augmentations of the octagonal prism: The uniform nonconvex great rhombicuboctahedron may be seen as an octagrammic prism with the octagrams excavated with crossed square cupolae, similarly to how the rhombicuboctahedron may be seen as an octagonal prism with the octagons augmented with square cupolae.
The pictures below show the excavation of the octagrammic prism with crossed square cupolae taking place one step at a time.
The pseudo great rhombicuboctahedron has a single "belt" of squares around its equator, and can be constructed by twisting one of the crossed square cupolae on a nonconvex great rhombicuboctahedron by 45 degrees.