What you really get serendipity is from re-encountering things you don't know or have forgotten. And we know how to predict if you have forgotten something: spaced repetition and the forgetting curve! To manufacture serendipity, you simply track 'flashcards' of important things, but optimize for the opposite of the normal spaced repetition goal: you want to review only things you are predicted to have forgotten by now.
https://gwern.net/note/statistic#program-for-non-spaced-repe...
Then, as a Remembrancer agent, you make it show preferentially items that are similar but you have probably forgotten. (The Remembrancer agent can be treated as a fraction of a review, on the grounds that even just showing you the title briefly can trigger serendipity and if it didn't provoke any reaction from you, then that is evidence it is not useful and that title should be downweighted and show up less.)
You can increase the odds, so that it is likely to happen more often. You can't engineer an instance of it. You can't compute it. If you could, it wouldn't be coincidence; it would be design!
The short end of it is something like: serendipity = work + telling people about the work