Use checkboxes instead of dropdown

[Troglos]

I've managed to replace the dropdowns with groups of checkboxes, but it works fine only if I choose 1 checkbox for taxonomy.

If my url is something like
"mysite.com/?facetious_post_type=products&rivestimento=trasparente&performances=antincendio&performances=antisismica&destinazione=corporate"
the result is obviously incorrect.

Any suggestion to get the right query?