A famous person in my hometown claimed that she was awarded a "1.5 Ph.D. degree" by her thesis committee in a famous law school in London in the early 1980s (which was noted on her diploma, according to her memoir) -- is there really such a thing in academia?
No. It is difficult to prove a negative, but the idea of a "1.5 PhD" seems far-fetched on its face. Negative search results on the internet coupled with the lack of answers here over the past six months further indicate that the answer is no.
Where did this crazy idea get started? Apparently, from some claims made by the President of Taiwan. As stated in this report by a faculty member at the University of North Carolina:
[President Tsai Ing-Wen] also claimed that the committee decided not just to award her a PhD in law in 1984, but also to add the remark “she has extraordinarily strong academic background in international trade” to her PhD diploma. She went on to say that the thesis committee lionized her work as “worthy of 1.5 PhD degrees.”
There was some controversy in 2019 about whether Dr. Tsai had earned a PhD at all (in fact, the linked report concludes in the negative). However, the London School of Economics confirmed that she was "correctly awarded a PhD in Law in 1984." The LSE did not mention anything about an "extra half PhD," nor is there any proof that the faculty added any remarks to her diploma (indeed, adding remarks to a diploma is not a typical practice).
I suspect that what happened is that her advisor made the remarks when introducing her at the defense, and she simply paraphrased and/or embellished those comments. Indeed, some commenters suggest that the introductions at public defenses tend to have "gushing praise," to the point where suggesting she deserves "merely" an extra half-PhD could be considered rather faint praise. I suspect this varies culturally; no one made such remarks at my defense or at others I attended (maybe we are just slackers...).
No, generally speaking - not a thing.
However, in many ex-Soviet countries a post-PhD degree called Doctor of Sciences exist. This is not to be confused with German "Dr. ..." system which is equivalent to PhD. So in Russia, for PhD the requirement would be having just 2 publications (3 for social sciences) while for Doctor of Sciences it is 10 (15). There you have it, "PhD 2.0". On top of that, there are precedents of PhD dissertations being so good a Doctor of Sciences degree was awarded for them instead even though other formal requirements were not met. So there is some far-fetched existing base for that (well, probably not particularly that very) claim, after all.