<page xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
      xsi:noNamespaceSchemaLocation="urn:magento:framework:View/Layout/etc/page_configuration.xsd">
    <update handle="customer_account" />
</page>

public function aroundExecute(MagentoCmsControllerPageView $subject, callable $proceed)
{
    $pageId = $subject->getRequest()->getParam('page_id', $subject->getRequest()->getParam('id', false));

    // Some code that determines whether or not this CMS page should have the dashboard navigation:
    if ( ... ) {
        // Add customer_account layout update:
        // This is the part that doesn't work...
        $resultPage->getLayout()->getUpdate()->addUpdate('customer_account');
    }

    return $resultPage;
}

<update handle="customer_account" />