[@Cottser answer works][1]. I just modified it to keep the right specificity using `array_splice`, otherwise the bundle type template gets applied later in the chain than block instance suggestions.

    $suggestion = 'block__' . $content['#block_content']->bundle();
    array_splice( $suggestions, 2, 0, $suggestion );

There is an issue to fix this in core for all entities

https://www.drupal.org/node/2270883


  [1]: http://drupal.stackexchange.com/a/171976/27987