As previously stated it is not possible, but even if it were it would be a miserable experience. It sounds amazing on paper but the world is far from a perfect place. You'd live through war time over and over again, you'd see people you love die of old age around you, and of course there's the scifi paranoid yet feesible concept of some government body discovering your existence whihc they would want to study. Death is what makes us appreciate life and you can't fight time. Eventually he takes us all.
Immortally... in some form, is achievable depending on your beliefs and abilities. While I won't go into detail I believe there are ways to remain active in this world after your body fails.
If you are able to gather and retain enough metaphysical/spiritual power upon death, combined with a strong will and knowledge of the other planes, you could be "immortal". Of course you would be considered a Traveler, or perhaps a Ghost, and require great effort to do anything on the physical plane, if you're lucky enough, let alone be able to communicate.
Now, on the subject of physical immortality. The kind that doesn't involvement losing either body, mind, or soul to remain "anchored". While science can potentially extend your mortal life you are doomed to die. You can only fix so many of your body's systems before too many breakdown. Perhaps, if you are willing to delve into my studies, you might be able to reach a level of enhanced-mortality. This is not the place to go into the details of my studies, but if you can learn to harness certain unseen realms and alter the interactions between your body, mind, and soul than you might be able to achieve your goal before dying. The things I might be able to help you learn will not stop your death, but rather allow you to function in a way that gives you a chance of doing something you might not achieve normally within your life.