I would assume that anything that could be morphed would need to:
A) Have some form of a nervous system. This does not rule out all incredibly small morphs; even copepods (a type of incredibly small zooplankton) have nerve cells. It does however, instantly rule out plants and fungi. A nervous system would be vital as to process conscious thought; there is no 'consciousness' without one, even if it is just the most simple of instincts. Without thought, they couldn't morph it, as they need conscious effort to do so. Even if morphing technology would allow one to acquire a plant, once they reach a point of no return, their mind will not exist outside of Z-space, and they would be trapped without being either conscious or aware of it.
B) Be multicellular. As in no bacteria, no protists and no unicellular fungi (which was already eliminated by A), and obviously viruses, which are not technically even considered a life form. This is a moot point to bring up, however, as point A already covers this, as a unicellular organism cannot possibly have a nervous system.