Hi Salvia,
Thank you for those kind words.
Unfortunately it is not as simple as editing some files. The core functionality of the filter is depending on that URL structure. What’s going on when you’re on a filtered page is that you are actually still at the regular post archive (mysite.com/post_type) but the filter appends some parameters (?taxonomy=term&taxonomy2=term2) which WordPress interprets and uses in it’s standard wp_query.
You can see how the taxonomies and terms are added to the wp_query by looking at the global $wp_query object in your archive.php file (after you’ve set a filter):
<?php global $wp_query; ?>
<pre><code><?php print_r($wp_query, true); ?></code></pre>
So what you want would not allow anyone to filter on multiple taxonomies at the same time since you cant do “mysite.com/term/term2” (which can be in different taxonomies or not). If that doesn’t bother you and you’re fine with the visitors only being able to filter on one taxonomy at a time you’d have to code your own version of this.
Then you can use the javascript submission version found in the wp_category_dropdown article (to avoid ppl trying to submit multiple taxonomies) and apply select2 by yourself. But using this plugin for it would be like breaking down a mountain in order to get to the eagles nest. It would be easier to climb the mountain yourself ?? (I never get do to cool analogies).