You can’t override template parts. Even if you could, you would have no way of knowing what template part you’d need to replace. A theme is only required to have an index.php file and there are no restrictions or naming convention for template parts.
Your options are to create a full template and leave it up to users to better integrate it with their theme (like Woocommerce does, for example), or add a filter to the_content() to customize the markup just within the output of the_content() function.
EDIT– you can override full templates from a plugin via the template filters.