Craft, combine two sets of entry objects. Then limit the merged set to those not already included.

gistfile1.txt

{% set stories = entry.featuredStories %}

{% set combined = [] %}
{% set idArray = [] %}
{% for story in stories %}
	{% set combined = combined|merge([story]) %}
	{% set idArray = idArray|merge([story.id]) %}
{% endfor %}

{% if entry.featuredStoryTags|length %}
	{% set tag = entry.featuredStoryTags %}
	{% if entry.featuredStoriesCount|length %}
		{% set limit = entry.featuredStoriesCount %}
	{% else %}
		{% set limit = 1000 %}
	{% endif %}
	{% set taggedStories = craft.entries.section('featuredStories').relatedTo(tag).order("RAND()").limit(limit) %}
	{% for taggedStory in taggedStories %}
		{% if taggedStory.id not in idArray %}
			{% set combined = combined|merge([taggedStory]) %}
		{% endif %}
	{% endfor %}
{% endif %}