any approach to get the both/and set will involve some step that the iNaturalist platform will not perform for regular users, as far as i know. how manual that step is will depend on how comfortable you are with programming. the observation-set-based approach requires some sort of comparison between 2 sets (finding either the intersection or difference), and the identification based approach requires either an aggregation + aggregated filter or a comparison of 2 sets (intersection).
it’s worth noting that the observation-set-based approach that i described above was some version of X = (A+B+X) - A - B, but you can simplify that as X = (A + X) - A or as X = (B + X) - B. you could also find X by comparing (A + X) and (B + X) and finding the intersection, and this is an alternative i didn’t describe earlier.
it’s possible someone has written a tool to find the both/and set that i’m not aware of, and it’s possible that there may be other ways to find the both/and set in specific situations. that said, without more knowledge about why you’re trying to get this information, it’s not possible to determine whether your use case is a special case that can be handled in a different way.