Is it possible to orderby multiple meta_keys when using meta_value_num?

You might want to check out the query improvements in WP 4.2 for ‘orderby’ and ‘meta_query’. Details are on https://make.wordpress.org/core/2015/03/30/query-improvements-in-wp-4-2-orderby-and-meta_query.

Try to name your meta_query clauses, then order by them.

Following code is untested:

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