One of the films which inspired me as a kid was Moontrap, the plot of which has something to do with Bruce Campbell and his comrade Walter Koenig bringing an alien seed back to earth.
Nothing ever happens on the moon
This alien (re)builds itself out of various biological and electromechanical parts.
The Moontrap robot
At one point the robot had a skillsaw end effector, not unlike the robot in this exquisite depiction of saw-hand prowess:
Cyborg Justice (Sega Genesis, 1993)
In that game—which I also played as a child—you could mix-and-match legs, torsos, and arms to create robots.
The later movie Virus had a similar creature to the one in Moontrap, and if I remember correctly, the alien robots in the movie *Batteries Not Included could modify and reproduce themselves from random household junk.
The ability for a creature to compose and extend itself is quite fascinating. Not only can it figure out what to do with the objects it happens to encounter, but it can adjust its mental models in order to control these new extensions.
I think that building yourself out of parts is only a difference in degree from tool use.
During the long watches of the night the solitary sailor begins to feel that the boat is an extension of himself, moving to the same rhythms toward a common goal. The violinist, wrapped in the stream of sound she helps to create, feels as if she is part of the “harmony of the spheres.” The climber, focusing all her attention on the small irregularities of the rock wall that will have to support her weight safely, speaks of the sense of kinship that develops between fingers and rock, between the frail body and the context of stone, sky, and wind. —Csikszentmihalyi 
Human tool use
Humans are perhaps the most adaptable of animals on earth (leave a comment if you know of a more adaptable organism).
Our action-perception system may have morphology-specific programming. But it’s not so specific that we cannot add or subtract from it. For instance, anything you hold in your hand becomes essentially an extension of your arm. Likewise, you can adapt to a modification in which you completely replace your hand with a different type of end effector.
Alternate human end effector
You might argue that holding something does not really extend your arm. After all, you aren’t hooking it directly to your nervous system. But the brain-environment system does treat external objects as part of the body.
We have always been coupled with technology. We have always been prosthetic bodies.
Something unique about hands is that they may have evolved due to tool use. Bipedalism allowed this to happen. About 5 million years after bipedalism, tool use and a brain expansion appeared . It’s possible that the homo sapiens brain was the result of co-evolution with tools.
Oldowan Handaxe (credit: University of Missouri)
The body itself is part of the environment, albeit a special one as far as the brain is concerned. The brain has no choice but to have this willy-nilly freedom of body size changes—or else how would you be able to grow from a tiny baby to the full size lad/gal/transgender you are today?
An example of body-environment overlap is the cutaneous rabbit hopping out of the body experiment .
The white cutaneous rabbit
The original cutaneous (==”of the skin”) rabbit experiment demonstrated a somatosensory illusion: your body map (in the primary somatosensory cortex) will cause you to report tapping (the “rabbit” hopping) on your skin in between the places where the stimulus was actually applied. The out of the body version extends this illusion onto an external object held by your body (click on figure below for more info).
Hopping out of the body (credit: Miyazaki, et al)
Some other relevant body map illusions are the extending nose illusion, the rubber hand illusion, and the face illusion.
Get Your Embody Beat
Metzinger’s self-model theory of subjectivity  defines three levels of embodiment:
First-order: Purely reflexive with no self-representation. Most uses of subsumption architecture would be categorized as such.
Second-order: Uses self-representation, which affects its behavior.
Third-order: In addition to self-representation, “you consciously experience yourself as embodied, that you possess phenomenal self-model (PSM)”. Humans, when awake, fall into this category.
Metzinger refers to the famous starfish robot as an example of a “second-order embodiment” self-model implementation. The starfish robot develops its walk with a dynamic internal self model, and can also adapt to body subtractions (e.g. via damage).
I don’t see why we can’t develop robots that learn how to use tools and even adapt them into their bodies. The natural way may not be the only way, but it’s at least a place to start when making artificial intelligence. AI has an advantage though, even when using the naturally inspired methods, which is that the researchers can speed up phylogenetic development.
What I mean by that is I could adapt a robot to a range of environments through evolution in simulations running much faster than real time. Then, I can deploy that robot in real life where it continues its learning, but it has already learned via evolution the important and general stuff to keep it alive.
The ancient art of cyborg hands
This natural adaptability that you have as part of your interaction with the world could also help you modify yourself with far stranger extensions than chainsaws and cyborg hands.
Well-designed cyborg parts will exploit this natural adaptability to modify your morphology, if you so desire. Perhaps the same scheme could work even with a complete body replacement, or a mind-in-computer scenario in which you may have multiple physical bodies to choose from.
 M. Csikszentmihalyi, Flow: The Psychology of Optimal Experience. New York: Harper Perennial, 1990.
 R. Leaky, The Origin of Humankind. New York: BasicBooks, 1994.
 M. Miyazaki, M. Hirashima, D. Nozaki, “The ‘Cutaneous Rabbit’ Hopping out of the Body.” The Journal of Neuroscience, February 3, 2010, 30(5):1856-1860; doi:10.1523/JNEUROSCI.3887-09.2010. http://www.jneurosci.org/cgi/content/full/30/5/1856
 T. Metzinger, “Self models.” Scholarpedia, 2007, 2(10):4174. http://www.scholarpedia.org/article/Self_models