Wordpress - Rewrite Rules for Multiple (more than 2) Taxonomies

You could try something like this:

function custom_rewrite( $wp_rewrite ) {

    $feed_rules = array(
        'product-category/(.+)/material/(.+)/color/(.+)'    =>  'index.php?product_cat='. $wp_rewrite->preg_index(1).'&pa_material='. $wp_rewrite->preg_index(2).'&pa_color='. $wp_rewrite->preg_index(3)
        'product-category/(.+)/color/(.+)'    =>  'index.php?product_cat='. $wp_rewrite->preg_index(1).'&pa_color='. $wp_rewrite->preg_index(2)
        'product-category/(.+)/material/(.+)'    =>  'index.php?product_cat='. $wp_rewrite->preg_index(1).'&pa_material='. $wp_rewrite->preg_index(2)
    );

    $wp_rewrite->rules = $feed_rules + $wp_rewrite->rules;
}
// refresh/flush permalinks in the dashboard if this is changed in any way
add_filter( 'generate_rewrite_rules', 'custom_rewrite' );

It may not work exactly as advertised, and you might need to do some regex modifications, but that's the general gist of what needs to be done (90% of the work).

You will need to flush the permalinks if you add/edit/remove this code, put it in functions.php or a custom plugin. You can flush permalinks by simply going into the admin area and re-saving the permalinks

As a sidenote, you may run into clashing issues if you start using heirarchies,

e.g. if you have a tshirts/small and a dresses/small category, and you use a URL such as /products-category/small/color/red you might not get the results you expected, e.g. small tshirts? or did you mean small dresses?

So beware of ambiguity

For future reference (like next year when I google and find my own question again) this can be converted into add_rewrite_rule() syntax by converting the keys in the $new_rules array into the $regex parameter of add_rewrite_rule() with the value as the $rewrite and 'top' as the $position.

add_rewrite_rule($regex,$rewrite, $position);

Or as an example of one of my requests from above:

function custom_rewrite() {

   add_rewrite_rule(
    'product-category/(.+?)/material/(.+?)/?$',
    'index.php?product_cat=matches[1]&pa_material=$matches[2]',
    'top'
    );

}
// refresh/flush permalinks in the dashboard if this is changed in any way
add_action( 'init', 'custom_rewrite' );

For some reason I was unsuccessful using regenerate_rewrite_rules as a hook/filter so switched to init.