The Stow N Go Hanging Travel Shelves from Grand Fusion Housewares are my new favorite packable multi-tier shelves.
The three-tier nylon-and-mesh shelving unit collapses atop its own integrated zippered packing cube (well, cuboid, since one side is rectangular in the large size), compresses with a push, then latches shut with built-in plastic clip buckles.
Stash the parcel in a carry-on or check-through bag. At your destination, unlatch, lift, and hang the preorganized system from a closet or shower rod or over a door via its two steel hanger hooks. The zippered bottom compartment is great for holding shoes en route; then use it for dirty laundry after hanging.
The unit comes in two sizes, both 11.8 inches deep (front to back) and 25.2 inches high when expanded. The large model is 17.7 inches wide, and fits in a standard wheel-aboard bag or any suitcase 20 inches or larger. The small is 11.8 inches wide and pops into a tote.