A few years ago, I found several uniform compounds of Euclidean tilings that were analogous to uniform polyhedra with cubic and dodecahedral symmetry. The faces follow trends: 4/n, 5/n, 6/n and 8/n, 10/n, 12/n. Analogs in hyperbolic space seem likely to exist as well.
Compound of two trihexagonal tilings (3.6.6/2.6):
Spherical equivalents: Siid (3.6.5/2.6), Tisso (3.6.4/2.6)
Compound of three trihexagonal tilings (6/2.6.6/2.6)
Spherical equivalents: Did (5.5/2.5.5/2), {4, 2}*3 (4.4/2.4.4/2)
Compound of four rhombitrihexagonal tilings (3.12/3.6.12/3)
Spherical equivalents: Gidditdid (3.10/3.5.10/3), Gocco (3.8/3.4.8/3)
Compound of three rhombitrihexagonal tilings (6.4.6/2.4)
Spherical equivalents: Raded (5.4.5/2.4), Rah (4.4.4/2.4)
Compound of four omnitruncated trihexagonal tilings (6.12.12/3)
Spherical equivalents: Idtid (6.10.10/3), Cotco (6.8.8/3)
There are also some where only the "outside" faces follow the trends. In these cases, I have underlined the faces following trends.
Compound of ∞ apeirogonal prisms (12/3.12/3.∞)
Spherical equivalents: Quit sissid (10/3.10/3.5), Quith (8/3.8/3.3)
Compound of ∞ apeirogonal prisms (4.12/3.∞)
Spherical equivalents: Quitdid (4.10/3.10), Quitco (4.8/3.6)