Specific template for a structure
I can't answer it clearly, but I did a workaround for something similar.

I've loaded the same template for my structure but gave my structure 2 entry-types(overviewPage, detailPage).

Both entry types loaded the same template but got handled differently. So my template for the structure looked something like this:

{% if entry.type == 'overviewPage' %}
  {% include 'snippets/content_overviewPage.html' %}
{% elseif entry.type == 'detailPage' %}
  {% include 'snippets/content_detailPage.html' %}
{% endif %}


I hope to see on this thread how other people handle this.