How to print all values of a multi-value field, except the first?
In field preprocessing this while loop which fills the field items doesn't get started if the first delta is removed:

  $delta = 0;
  while (!empty($element[$delta])) {
    $variables['items'][$delta]['content'] = $element[$delta];
    $delta++;
  }


So if you bypass the field template to print the 0 delta do the same with the other deltas:

{# print first field value #}
{{ content.field_foo.0 }}
{# print something else #}
&lt;hr&gt;
{# print remaining field values #}
{% for key, item in content.field_foo if key &gt; 0  %}
  {{ item }}
{% endfor %}