What is the best method of creating morphs in a object created in blender?

I made a cat bed. Would like to make depressions in the surface. To correspond to a cat model's pose. Have tried with sculpting. Had a hard time controlling the brush. Is it possible to use soft body physics? To more or less lower the cat model onto the bed model to make the depressions? Or is there other options that might work better? Looking for options.

Rendered in Poser 11.

Poser Pro 2010