Filtering on related entries (with an array query param)
This should take care of it:

{% set stage = craft.request.getParam('stage') %}

{# check if stage is an array #}
{% if stage is iterable %}

    {% for stageItem in stage %}

        {# make sure stageItem has content #}
        {% if stageItem is not empty %}

            {{ stageItem }}
            {# would output the selected stage.value #}

        {% endif %}

    {% endfor %}

{% endif %}