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In Episode III, Anakin accepts Palpatine as his master and turns to the darkside in a desperate attempt to save his wife from dying. We know by their eventual deaths that they never truly discover Darth Plagueis' methods for cheating death but I'm curious how much time they spend trying to unlock his secrets.
It seems reasonable that they would spend a considerable amount of time on this given it was their original agreement when Anakin turned. Even though Padme had already been lost, I would think Vader would still be interested in keeping himself or anyone else he wanted from dying.
I know that in Legends canon Sidious is able to transfer his spirit into a new body but this isn't exactly what Darth Plagueis was doing. Plus, I'm more interested in Sidious' joint efforts with Vader, given their original agreement to search together. Are there any sources (Disney Canon or Legends) that dive into their research?
EDIT: For clarification, I'm aware of questions like this: Did Darth Sidious and Vader ever discover how to cheat death?. They mention the discovery (which I kind of don't count anyway since it was Palpatine by himself and not really the same thing as what Plagueis did) but talk nothing of the research, the agreement between Vader and Sidious, or Vader's motivations after Padme's death which are what I'm interested in. To be clear, I want to know if Vader and Palpatine looked for Plagueis' secrets together.
If the emperor learning to transfer his essence from body to body is the best there is, then I'd like to know more about the research and anything about what this meant for Vader and their agreement.
I also edited the title of my question to more accurately represent how my question is different from the suggested duplicate.