Subtheme for Subsite in Multisite
In Drupal 8 you are supposed to organize your themes and multi-site instances like in the following structure. I only highlight the relevant folders.

__docroot
  |__modules
  |  |__contrib
  |  |  |__devel
  |  |  |__views
  |  |__custom
  |     |__my_module_abc
  |     |__my_module_xyz
  |__sites
  |  |__default
  |  |  |__settings.php
  |  |__site1
  |  |  |__settings.php
  |  |__site2
  |     |__settings.php
  |__themes
     |__contrib
     |  |__bootstrap
     |__custom
        |__my_bootstrap_subtheme


So, if you want to create a sub-theme of a custom theme, you also have to place it inside docroot/themes/custom. Then it will appear in your back-end where you can enable it.



But what I would recommend instead of adding another sub-theme, is to simply add a template suggestion based on the multi-site instance name via hook_theme_suggestions_HOOK_alter. By that you can move on with only one custom theme (which is much easier to maintain in the end), and inside its MYTHEME.theme file you'll switch the page template for your certain multi-site instance like following.

/**
 * Implements hook_theme_suggestions_HOOK_alter().
 */
function MYTHEME_theme_suggestions_page_alter(array &amp;$suggestions, array $variables) {

  $site_path = \Drupal::service('site.path');
  $site_path = explode('/', $site_path);
  $site_name = $site_path[1];

  $suggestions[] = 'page__' . $site_name;
}


Now you simply can place page--site1.html.twig in your theme's template folder and site1 will take this page template instead the default page.html.twig. (Source)



Tried it on a fresh D8 with Twig debugging enabled and it works just fine.

&lt;!-- THEME DEBUG --&gt;
&lt;!-- THEME HOOK: 'page' --&gt;
&lt;!-- FILE NAME SUGGESTIONS:
   x page--site1.html.twig
   * page--front.html.twig
   * page--node--1.html.twig
   * page--node--%.html.twig
   * page--node.html.twig
   * page.html.twig
--&gt;
&lt;!-- BEGIN OUTPUT from 'themes/custom/my-custom-subtheme/templates/page--site1.html.twig' --&gt;