Refine/Filter WP_Query Posts with jQuery or Ajax

I think what you might be looking for is combination of a plugin like https://wordpress.org/plugins/query-multiple-taxonomies/ and hooking into pre_get_posts if you are looping a list of posts. That plugin is in use on http://theboatworksnews.com/ so you can play with the projects section/filters and see if that matches what you’re looking for.