You could add a new entry type "Duplicate" to your section with just an entries field "Use content from entry".
In your template you can now overwrite your entry
variable with:
{% set entry = entry.type == 'dupe' ? craft.entries.id(entry.contentFrom.first().id).first() : entry %}
You could also use the "Duplicate" entry type to link to the same entry / URL twice from your navigation:
{% nav entry in entries %}
{% if entry.type == 'dupe' %}
{% set entry = craft.entries.id(entry.contentFrom.first().id).first() %}
{% endif %}
<a href="{{ entry.url }}">{{ entry.title }}</a>
{% endnav %}
And in case someone "guesses" the URL, simply redirect them to the original entry:
{% if entry.type == 'dupe' %}
{% set entry = craft.entries.id(entry.contentFrom.first().id).first() %}
{% redirect entry.url %}
{% endif %}