Is it possible to orderby multiple meta_keys when using meta_value_num?

Question

Reading through the order & orderby documentation, it's not clear to me whether there is any support to order based on multiple meta_key values.

Obviously, using meta_query I can return posts based on multiple key-value pairs, but I want to be able to control the order that these results are returned based on multiple meta_keys.

For example, I have pages that have multiple categories and each category has a numerical rank. If a user is searching for pages that are in one of three different categories, I can return all the necessary posts with the following:

$query = array(
  'order' => 'DESC',
  'orderby' => 'meta_value_num',
  'meta_query' => array(
    'relation' => 'OR',
    array( 'key' => 'cat1', 'type' => 'numeric' ),
    array( 'key' => 'cat2', 'type' => 'numeric' ),
    array( 'key' => 'cat3', 'type' => 'numeric' )
  );
);

However, once those are returned, I would like them to be ordered based on the highest numerical value across any one of the categories that results were returned on. In other words, posts with a 9 value in cat1 would appear around the same order as posts with a 9 value in cat3.

Looking at this answer it seems that a meta_key isn't even necessary for 'orderby' => 'meta_value_num', but that doesn't match the documentation for meta_value, which is far more documented than meta_value_num... Any clarification would be useful. Thanks!