D8 - Implements form inner wrapper with suggestions so form elements can be rearranged.

MY_THEME.theme

<?php

/**
 * Implements hook_form_alter().
 *
 * @param $form
 * @param \Drupal\Core\Form\FormStateInterface $form_state
 * @param $form_id
 */
function MY_THEME_form_alter(&$form, \Drupal\Core\Form\FormStateInterface $form_state, $form_id) {
  // If #theme is set we test if it's a string. If it's a string we convert to
  // array so we can append our base theme. If no #theme was specified by initial render
  // array, FormBuilder adds $form_id and $form_base_id to #theme array.
  if (isset($form['#theme'])) {
    if (!is_array($form['#theme'])) {
      $form['#theme'] = [
        $form['#theme'],
      ];
    }
  }
  $form['#theme'][] = 'form_inner';
}


/**
 * Implements hook_theme_suggestions_alter().
 *
 * @param array $suggestions
 * @param array $variables
 * @param string $hook
 */

function MY_THEME_theme_suggestions_alter(array &$suggestions, array $variables, $hook) {
  switch ($hook) {
    case 'form_inner':
      // Add suggestions for provided #theme hooks.
      foreach (array_reverse($variables['form']['#theme']) as $theme) {
        if ($theme !== $hook) {
          $suggestions[] = $hook . '__' . $theme;
        }
      }
    break;
  }
}

/**
 * Implements hook_preprocess_HOOK().
 *
 * @param $variables
 */
function MY_THEME_preprocess_form_inner(&$variables) {
  // We unset #prefix and #suffix if they were provided because
  // forms #theme_wrapper which invokes theme 'form' already has
  // rendered #prefix and #suffix.
  if (isset($variables['form']['#prefix'])) {
    unset($variables['form']['#prefix']);
  }
  if (isset($variables['form']['#suffix'])) {
    unset($variables['form']['#suffix']);
  }
}

/**
 * Implements hook_theme().
 */
function MY_THEME_theme() {
  // Define default theme for form inner wrapper.
  return [
    'form_inner' => [
      'render element' => 'form',
      // If you like to keep your templates structured in folder, keep 'path'
      // property, otherwise remove it.
      'path' => drupal_get_path('theme', 'MY_THEME') . '/templates/form',
    ],
  ];
}

templates@form@form-inner.html.twig

{#
/**
 * @file
 * Default theme implementation for a 'form_inner'.
 *
 * Available variables
 * - form: Contains form elements.
 *
 * @see template_preprocess_form_inner()
 *
 * @ingroup themeable
 */
#}
{{ form }}