Replicate UI: Let user fill out more fields than just title on Replicate Confirm form

Hi, I need exactly the same. Instead of just changing the label / title, I need the option for the editor to choose the correct bundle from my custom entity. Is this somehow possible?

Thanx again @texas-bronius for your initial comment. I think I were able to find a working solution for my "NON translatable" custom entity.
Within a custom module, I added

use \Drupal\Core\Form\FormStateInterface;

function mymodule_form_alter(&$form, \Drupal\Core\Form\FormStateInterface $form_state, $form_id) {
  if ($form_id == 'MYCUSTOMENTITY_FORM_replicate_form') {
    $form['new_bundle'] = [
      '#type' => 'select',
      '#title' => t('Bundle Type'),
      '#default_value' => 'unuiqe',
      '#options' => ['global' => t('Global'), 'unique' => t('Unique')],
      '#description' => t('Select the target bundle type'),
      '#weight' => -1,
    ];
    array_unshift($form['actions']['submit']['#submit'], '_mymodule_replicate_form_submit');
  }
}

function _mymodule_replicate_form_submit($form, FormStateInterface $form_state) {
  $entity = $form_state->getFormObject()->getEntity();
  $bundle = $form_state->getValue("new_bundle");
  $entity ->set('bundle', $bundle);
}

Hope this is the right way of implementation ;-)