Is it possible to add a button to a field_collection?
I ended up asking Sacrilegious, one of the regulars in #drupal-support, and he offered this solution:

Define a new class in {module root}\Plugin\Field\FieldWidget names FieldCollectionCustomEmbedWidget.php

&lt;?php

/**
 * @file
 * Contains \Drupal\{module}\Plugin\Field\FieldWidget\FieldCollectionCustomEmbedWidget.
 */

namespace Drupal\{module}\Plugin\Field\FieldWidget;

use Drupal\Core\Field\FieldItemListInterface;
use Drupal\Core\Form\FormStateInterface;
use Drupal\Core\Render\Element;
use Drupal\field_collection\Plugin\Field\FieldWidget\FieldCollectionEmbedWidget;

/**
 * Plugin implementation of the 'field_collection_custom_embed' widget.
 *
 * @FieldWidget(
 *   id = "field_collection_custom_embed",
 *   label = @Translation("Embedded custom"),
 *   field_types = {
 *     "field_collection"
 *   },
 * )
 */
class FieldCollectionCustomEmbedWidget extends FieldCollectionEmbedWidget {

  /**
   * {@inheritdoc}
   */
  public function formElement(FieldItemListInterface $items, $delta, array $element, array &amp;$form, FormStateInterface $form_state) {
    $element = parent::formElement($items, $delta, $element, $form, $form_state);

    $element['custom_button'] = [
      '#markup' =&gt; '&lt;div class="guess-compatibility js-form-button field-add-more-submit button js-form-submit form-submit"&gt;button text&lt;/div&gt;',
      '#value' =&gt; t('button text'),
      '#attributes' =&gt; [
        'class' =&gt; [
          'my-custom-button-class'
        ],
      ],
    ];

    return $element;
  }
}


Then under Structure, I went into the settings for the form containing the field that needed this button, and under "Manage Form Display", I changed the widget type of the field to the newly added "Embedded Custom." Now the button is there.