Well, I'm not so sure I would go so far as calling them plans.
Basically it revolves around immortality, the immortality of one or two people as opposed to society as a whole. (I don't want to get into the problems that would arise if everyone could live forever... Ugh. We'd have to start uploading brains onto a motherboard and taking turns in a few surrogates.)
So one person retains life throughout the progression of humanity. First off is the question of how immortality is gained. Here my thoughts meet a first cross-road, some travelling down a path mysticism and mythology (Think: Osiris, fountain of youth, even touching on life-after-death and reincarnation) and others staying basically scientific. I guess that pretty much restrains possibilities to some form of transhumanism un- OH FUCK ETERNAL JELLYFISH NVM.
Yeah. Then you have to think about how lasting the immortality would be... If you get chopped into to pieces do you remain alive? Do you regenerate or do you have to find each part and put yourself back together? Or do you just die. Are we dealing with that lame pseudo-immortality that only grants eternal youth and health, allowing you to get killed by a gunshot? Hell no. Maybe you can be killed by something extreme, but you need at least a crazy high healing factor. Or some form of invulnerability.
Now, the question becomes what's more important to preserve? Body or mind? Mind, okay. So we need something that takes into account your brain and stops it from aging. Also some method to retain more memories, or like a really huge scrapbook. But generating synapses all over will possibly render you insane/ more ADHD than you already are... I don't actually know what the effects would be.
Now mind is great but I still dont want to be stuck in a rotting corpse. So either I need really great preservation or a series of surrogates or some kind of body-snatching skill or an artificial vessel. Now if I keep thinking artificial body# surrogates I get into the design field. Would I want to look the same or swap styles occasionally? Human, humanoid or something crazy out there? (I'd like to be a whale...)
Okay, then there's the whole dealing with everyone else dying and stuff. This is where survivor guilt comes in, especially if something happens and you end up the last person alive. Or whatever. Or, on the supernatural side of things, I'm pretty sure the most badass way to get immortality would be to kill like a city-full of innocents and absord their life force. Though I guess that would make you a sadistic bastard so you wouldn't care anyways...
And would somebody more likely become bitter and jaded or start enjoying life to the fullest? Would they flaunt their immortality or hide it? If hide, how would they cope with the endless changes in location they'd have to undergo. Or names. It's likely some identity shedding would be going on, unless you have a name that's really timeless. (I say get rid of letters all together. Call me 56.)
Then there's the whole what would you do with your time? My favourite answer is take over the world, establish an iron dictatorship, leave the establishment, rally the people to defeat it, repeat. Eternal challenge. Though one would have to be a bit of a psychopath.
So yeah.