As we all know, once a paper has been published in some form (whether or not in a peer-reviewed format), most journals will balk at the idea of publishing it again. Does this apply solely to publishing a work, or does this also apply to the entire idea of peer review?
If someone has already published a finding in a non-peer reviewed venue (e.g. popular magazine, trade paperback, newspaper, radio broadcast, etc.), and then later realizes that the findings would have been significant enough for a scientific publication, is there a process by which they can "go back" and get the peer review that they realize they should have gotten? E.g. a person could then claim:
I published this in 2015 as an article in The New York Times, but in 2018 I paid Science $10,000 to peer review it and they gave me a piece of paper saying that it is 100% Genuine Science (TM) and would have been published by them had it not already been published elsewhere. For this reason, my article can be cited as a peer-reviewed paper (or "equivalency") and should count toward qualifying for faculty positions, even if Science did not actually physically publish it. Please cite me as "Columbia, R. (2015 Jan 12), Radical Deconstruction of Spline Reticulation in Eightspace with reference to Post-Modern Patriarchy, New York Times, Peer Reviewed Science Aug 6, 2018."
Is there a general procedure for handling such cases? Will a journal do this if you pay them a reasonable amount of money to cover expenses and profit? Are there non-publishing academic institutions that specialize in the service of peer reviewing existing publications and giving them their Stamp of Good Science Approval? Is this technically possible but extremely rare or nearly unheard-of?
I found this question : Can non-peer-reviewed work be recognized by the community? , but it seems to more be asking about getting non-peer reviewed results de-facto accepted by the scientific community over time rather than about how to get a formal one-and-done post-publication peer review.
In summary, I'm not asking whether or not a paper already published in a non-peer reviewed venue can later be published in a peer-reviewed journal. I'm asking whether or not a paper already published in a non-peer reviewed venue can later receive peer review and be "upgraded" in status to a "real" academic publication without needing to be republished. Whether or not any particular non-peer reviewed publication meets, or even has a remote chance of meeting, the standards of peer review is out of scope.