Stop exposed filters from rewriting url to begin with taxonomy/term/all
Assuming Drupal 7.x and Views 3.x.

Edit the View. In the filter config, make sure the "Allow multiple selections" option is ticked. Without that, you've configured the filter to only allow a single option per filter.

If "country-animals" is setup as a contextual filter, you'll need a patch from this issue to allow multiple terms.

Hope that helps.