Views with both menu and jump menu taxonomy terms as contextual filters
I'm editing my response based on your latest comment!

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One way I think you can do what you're trying to do is incorporate facets into your page with those specific taxonomy terms placed on the page as facets.

You'd need to use the Facet API module and the Faceted Navigation for Search module.  You can see the module page for an example interface - do you see how the screenshot on the module page shows a site where you can narrow the results based on fields/facets on the side?  I'm adding a screenshot from a site of my own that I've set up to use facets, though it's themed very differently.  The other great thing about facets is that they show you how many nodes you have tagged with the fields/terms you want to filter on.



Essentially, what facets do is give you the ability to FILTER/narrow listings based on select-type fields or taxonomy terms.  You can combine these filters, just as you describe.

I've only used the facet api with solr search, not core drupal, so I don't know if I can help you much on the exact setup, but perhaps this can at least guide you into another potential way to achieve your goal (if it's not overkill to learn all about facets and how you may be able to do this through search).  

Let us know how it works out or if you figure it out!