What about ones of the ones from dogshowtrolleys.com they look bit and bulky but actually fold down flat.
See
link not the actual site ut good for pic of this bigger model
If you scroll through the pics you will seen what i mean about the collapse. We sold ours when we changed breed but ours was a small so 2 compartments and the top for stuff and collapsed it wedge in the back seat foot well up the back of my seat when we were really packed in with people and dogs.
Heres a link to the one we had
link they come apart even more these days if you look at the assembly bit