Consolidate Metaboxes into 1 Big Metabox

Register your taxonomies with 'show_ui' => false, and then add a single meta box to manage them.

function create_book_tax() {
        register_taxonomy(
                'genre',
                'book',

                array(
                        'label' => __( 'Genre' ),
                        'rewrite' => array( 'slug' => 'genre' ),
                        'hierarchical' => true,
                        'show_ui' => false,
                )
        );
}

Or unhook the boxes from the side panel and put them below the main editor (using a post type and tax form the docs).

add_action(
  'add_meta_boxes_book',
  function () {
    remove_meta_box( 'genrediv', 'book', 'side' ); 

    $tax_name="genre";
    $taxonomy = get_taxonomy( $tax_name );

    $label = $taxonomy->labels->name;
    $tax_meta_box_id = $tax_name . 'div';

    add_meta_box( 
      $tax_meta_box_id, 
      $label, 
      $taxonomy->meta_box_cb
    ); 
  }
);

A third option is to create your own set of meta box containers and add your boxes to those.

add_action(
  'add_meta_boxes_book',
  function () {
    remove_meta_box( 'genrediv', 'book', 'side' );
  }
);

add_action(
  'dbx_post_sidebar',
  function ($post) {

    $tax_name="genre";
    $taxonomy = get_taxonomy( $tax_name );

    $label = $taxonomy->labels->name;
    $tax_meta_box_id = $tax_name . 'div';

    add_meta_box( 
      $tax_meta_box_id, 
      $label, 
      $taxonomy->meta_box_cb,
      'book',
      'mycol1'
    ); 

    echo 'my boxes'; //debug
    do_meta_boxes('book', 'mycol1', $post);
    do_meta_boxes('book', 'mycol2', $post);
    do_meta_boxes('book', 'mycol3', $post);
    echo 'end my boxes'; //debug
  }
);

If you look at the source you will see that the containers you created are surrounded by divs with the mycol*-sortables id. You should be able to use that to create the columns you are after.