Imagine yourself (A) and two other bodies similar to yours grown without brains (B and C). Transmitters are added to B and C So A can feel what they feel stimuli to there body and perhaps see what B and C could see. Brain mass is added to B and C connected wirelessly to A. More and more connections are added, and more brain mass is added to B and C. A can now control and feel bodies B and C and can think using B's and C's brain (if the wireless brain connections are problems you can imagine A being physically connected to B and C by many tubes of brain mass). Now the brain tissue in your body (A) is slowly removed which is fine because B and C are developed enough to run without A. You begin to perceive what A perceives less and less but can perceive what B and C perceive just fine. More and more of your thinking is done in body B and C. Eventually body A is completely gone so C no longer knows what B is thinking, and B no longer knows what C is thinking.
If you (at first A then B-A-C then B and C) wished to continue its consciousness there is little question you achieved your goal. But now there are two of you, and B no longer has to care if C lives on and C no longer has to care if B lives on. B and C can both claim their consciousness continued through the transformation and that they are indeed the same person A was. This could be done to create any number of copies and the reverse procedure could be used to merge two concsiousness to make one. So would A have been satisfied if just one of these copies went on to live forever? Once you became B he would only care about copies made of B and not about C. So your veiws of what you
want to continue would change when you become transformed into B and C. In fact you as B would have similar opinions of the importance of C as you would if C was a copy of yourself without continuity of consciousness (perhaps a quantum MWI copy). If you were copied 10^50 times by the procedure above would you still exist if all but one died? Surely you would from the perspective of that one, and surely you wouldn't from the perspective of the others.
