Query ‘orderby’ when there are multiple values for the same meta_key

Sorting by multiple meta keys (ref) may be helpful (untested):

add_action( 'pre_get_posts', function ( \WP_Query $query ) {
    $orderby = $query->get( 'orderby' );

    if ( 'start_date' === $orderby || 'end_date' === $orderby ) {
        $meta_query = array(
            'relation' => 'OR',
            'meta_query_1' => array(
               'key' => $orderby, // start_date or end_date
            ),
            'meta_query_2' => array(
                'key' => 'dates_date',
            ),
        );

        $query->set( 'meta_query', $meta_query );

        // Play with this.
        $query->set( 'orderby', array(
            'meta_query_1' => 'ASC',
            'meta_query_2' => 'DESC',
        ) );
    }
} );