Featured request: Search filter to display only certain categories

I had a chat with a user (follow up on 1191876-zen) who's using Jetpack for the Search module only.

They're about to launch their new site and would like to know if there's a way to get a filter that displays only certain categories when researching for a specific word by keeping the posts within the categories that aren't fetched by the search engine.

For example, imagine I have 4 posts resulting after I searched for 'lorem ipsum'. They are labeled under different categories (`ABC`, `LMN`, `XYZ`, and ~HJK`), but I'd like the search feature to search for keywords only on "XYZ" and "HJK" as opposed to the entire range of categories created to sort the posts.

Do you think that'd be doable? Upon checking on the current hooks, it seems like this one is not in there.

cc @gibrown - Thanks for checking on that