Let’s start with term archive concept and works backwards. It is easy for human to grasp it — it’s an archive with posts having particular term.
On a more technical level though — it’s a combination of query variables, which “tells” WordPress it is such archive. So if we dump query variables there will be variable designating the specific term posts should have.
And where do query variables come from? From the URL. Rewrite process turns URL (using rules configured) into query variables.
Now this process can actually be replicated from scratch (not by any means easily unfortunately). Needing specific kind of archive (or maybe even not quite archive) we can come up with query variables that produce it and rewrite rules for URLs that will result in those query variables.
It’s relatively rarely done (it is convoluted part of WP core), so there aren’t that many materials around. The closest I can think of for your description would probably be what Advanced Taxonomy Queries with Pretty URLs blog post describes.