Theoretically Plagueis was able to achieve immortality not by keeping his body alive, but by transfering his counscious into younger bodies down the centuries. He trained Sidious as an apprentice, and when he perceived his own power was finally weaker than his subordinate, used his powers to switch bodies. Then Plagueis-in-Sidious' body killed a surprised and weakened Sidious-in-Plagueis body.
Anakin was very powerful, and Plagueis selected him for his next body replacement. When Anakin made the transfer to Vader (due to a liberal application of lightsaber wounds due to Obi-Wan), Plagueis realized he no longer had a replacement because Anakin's body was a wreaked shell, that would offer no long-term gains. This changed when Luke came along, but we know how that went with Plagueis-in-Sidious/Palpatine's body falling down the bottom of the death star...
BUT somehow Plagueis's concious survived, maybe he transferred it to another body somehow? Maybe he didn't die at the base of the death star (i mean, look at Darth Maul, he didn't die after a huge fall and he was
cut in half!) and was able to survive in a new body, now controlling the "First Order" under the guise of "Supreme Leader Snoke." But in reality he is Plagueis all along.
And now, Plagueis/Snoke intends to transfer his conscious into a new body, that of Kylo Ren, and continue the cycle? Maybe by taking that girl jedi's body at some point? Or maybe he has been lusting after Skywalker for so long, maybe that is why he was searching for him all this time? The body he was promised but never achieved?
This is all just a big conspiracy theory of course.
