Anesthesia argument is that when the functioning of the brain changes enough do to drugs that are given to cause unconsciousness you are gone. This does not mean that your body is gone or the soul that is supposed to be connected to the body is gone. Your body is not you. Your soul is not you. You are consciousness that is produced by the correct structure and functioning of a brain.
It is not only the functioning of the brain the produces you, it is the right functioning of the brian that produces you. Because the brain is still functioning when anesthesia type drugs are given, but the brain is functioning differently than when you were consciousness. Anesthesia type drugs act in a continuum fashion; a small amount of the drug will have a small effect on consciousness. Increase the amount and you increase the effect. This shows that the brain slowly malfunctions do to the increasing amount of the drugs thus you slowly loose consciousness with increasing amounts of the drug or drugs.
Experiments with Anesthetic drugs have been done over and over again. Someone might argue that you are still conscious but you do not remember it. Since loosing and regaining of consciousness can be a gradual thing that can effect different parts of the brain at different times and stages it seem that you certainly could be conscious and your memory of being conscious is impaired. But because the type and amount of functioning of the brain can change and is a gradual continuum type process there will always be a point where the functioning is restricted enough where there is no consciousness produced. This has been shown when the brain functioning is observed by different means when anesthesia is used.
It is also possible that the brain is still producing consciousness but not a consciousness that you experience. So anesthesia my change the brains functioning enough so that the ixperiencitness changes to someone else's consciousness or something else's consciousness.
If you do not experience anything when you are under the influence of anesthesia does this not mean that you are the structure and functioning of this particular body and no other body. How do you know that you are not experiencing anything else?
What would be the evidence of the multiplicity of your ixperiencitness existing at the same time? There is no necessary conscious connection between what one body produced in terms of ixperiencitness and consciousness and what another body produces except in identity, approximation, or conscious observation and experiential observation. For you to experience the experiences of others having your consciousness and ixperiencitness you have to have the structure and functioning that produces these types of experiences which is beyond what your brain is producing now.
Anesthesia extension argument is a continuation of the Anesthesia argument where we see what happens when we make changes to the body while there is no consciousness being produced.