To be not so cheeky, I am giving a detailed answer for the following multiple version of PR-theorem.
Theorem: For any countable sequence $\{\mathbf{a}_n\}_{n\in \omega}$ non-zero Turing degrees, there is some degree $\mathbf{g}$ so that for any $n$, $\mathbf{a} _n\vee \mathbf{g}=\mathbf{g'}$.
I know four proofs of the theorem.
The first is by a slightly modification of Posner-Robinson's original argument. It was Joe who told me that $\Delta^0_2$ version of the theorem can be found in the P-R's original paper. Then Frank Stephan observed that, by a slight modification of their method, one may obtain the (almost-)full version.
The second proof is about Jockusch-Shore style proof, which is due to Kirill Gura, who was an undergraduate student in Madison. I learned the proof from Joe too. In Kirill's proof, a notion called Kalimullin pair, which is from the $e$-degree theory, was used.
The third proof is due to Stpehan, Tanuwijaya, Yang and me. It is also a Jockusch-Shore style proof. The key fact we used is that for any countably many non-zero degrees, each of them contains a set so that the union of them is immune but the intersection is infinite.
The fourth-proof is due to Slaman. And it is a pretty straightforward application of Kumabe-Slaman forcing. The proof can also be found in Kirill's draft.
Notice that $\mathbf{g}$ can be 1-generic in the both the second and third proofs. And no way in the other proofs. Ted told me that he and Kucera tried very hard to find a method to replace Kumabe-Slaman forcing, which, so far, has very limited applications such as to prove higher P-R theorem.
I got interested in the theorem when I was in a Dagstuhl meeting in 2017. Joe told me that he was thinking about a question, which was raised by Andrew Marks, about simultaneously randomness relative to multiple-degrees. Then I just recognized that maybe a multiple version of PR-theorem useful. Then he told me that it is already in P-R's paper.
That was all I remember.