Using "Search Within Results" in filters
or "Any Field" in the work search
Throughout the following tutorial, I refer to the Search Within Results field of the filters menu. These techniques also apply to the Any Field box in the work search form.
When you look at any tag on AO3, you'll have access to the filters menu. It will either appear on the right hand side of your screen if you're on a laptop, or it will pop out if you press the Filters button on a mobile device.
Down near the bottom of that menu, you can see a box labelled Search Within Results. This box allows you to search for specific terms in a fic's title, summary, author's note, and/or tags.
This field uses Boolean search terms: AND, OR, and NOT. Those words (the capitalization is important) combine with keywords to create more specific searches. You can also make use of the specific ID number associated with each tag. This reduces the text you need to type in, and it also accounts for all of the synonyms of a tag instead of just an exact text match.
I have a tutorial for finding the tag ID number over here.
You can enter as many keywords or terms into the box as you'd like, although there is a point at which the resulting browser url (which contains all of your filters) maxes out and the browser can no longer load your results. It hasn't happened to me, personally, but I've heard stories.
One example of how to use tag ID numbers to build out a results page of what you want to read is the following:
relationship_ids: 66194032 OR relationship_ids: 75960384 NOT relationship_ids: 66351727
The first ID is for Kip Grady/Scott Hunter, the second is for Ilya Rozanov & Svetlana Vetrova, and the third is for Shane Hollander/Ilya Rozanov.
This tells AO3 that I want to see fics that are tagged with either the first relationship or the second relationship, but I don't want to see fics with the third relationship (even if the other ships are tagged).
I'll still see fics tagged with Shane & Ilya or with any other relationships in Heated Rivalry, so long as either Kip/Scott or Ilya & Svetlana are tagged. I'll also see results with both Kip/Scott and Ilya&Svetlana tagged.
Where you are when you enter the filter will change how many results you see. So for example, if I enter this into the Search Within Results filter while I'm already looking at the Heated Rivalry (TV) tag, I won't get any results from the Game Changers Series - Rachel Reid unless Heated Rivalry (TV) is tagged too. That gets me 757 works.
I can enter it into the Any Field on the Works Search page to get all of the results from all fandoms, and then my results increase to 848 works.
You can also search for fandom_ids, character_ids, creator. Just combine your search terms with AND, OR, and NOT to specify if the term must appear, may appear, or must not appear in your results.
For more information on Search Within Results, I recommend this three-part news post from 2013.