Using this class, you can have drop-down lists with "multiple" property.

multiple-dropdown-categories.php

<?php

defined( 'ABSPATH' ) || exit;

/**
 *
 */
class YWP_Walker_CategoryDropdown extends Walker {
	/**
	 * What the class handles.
	 *
	 * @since 2.1.0
	 * @var string
	 *
	 * @see   Walker::$tree_type
	 */
	public $tree_type = 'category';

	/**
	 * Database fields to use.
	 *
	 * @since 2.1.0
	 * @todo  Decouple this
	 * @var string[]
	 *
	 * @see   Walker::$db_fields
	 */
	public $db_fields = array(
		'parent' => 'parent',
		'id'     => 'term_id',
	);

	/**
	 * Starts the element output.
	 *
	 * @param  string   $output             Used to append additional content (passed by reference).
	 * @param  WP_Term  $data_object        Category data object.
	 * @param  int      $depth              Depth of category. Used for padding.
	 * @param  array    $args               Uses 'selected', 'show_count', and 'value_field' keys, if they exist.
	 *                                      See wp_dropdown_categories().
	 * @param  int      $current_object_id  Optional. ID of the current category. Default 0.
	 *
	 * @see   Walker::start_el()
	 *
	 * @since 2.1.0
	 * @since 5.9.0 Renamed `$category` to `$data_object` and `$id` to `$current_object_id`
	 *              to match parent class for PHP 8 named parameter support.
	 *
	 */
	public function start_el( &$output, $data_object, $depth = 0, $args = array(), $current_object_id = 0 ) {
		// Restores the more descriptive, specific name for use within this method.
		$category = $data_object;
		$pad      = str_repeat( '&nbsp;', $depth * 3 );

		/** This filter is documented in wp-includes/category-template.php */
		$cat_name = apply_filters( 'list_cats', $category->name, $category );

		if ( isset( $args['value_field'] ) && isset( $category->{$args['value_field']} ) ) {
			$value_field = $args['value_field'];
		} else {
			$value_field = 'term_id';
		}

		$output .= "\t<option class=\"level-$depth\" value=\"" . esc_attr( $category->{$value_field} ) . '"';

		// Type-juggling causes false matches, so we force everything to a string.
		if ( is_array( $args['selected'] ) ) {
			if ( in_array( (string) $category->{$value_field}, $args['selected'] ) ) {
				$output .= ' selected="selected"';
			}
		} else {
			if ( (string) $category->{$value_field} === (string) $args['selected'] ) {
				$output .= ' selected="selected"';
			}
		}
		$output .= '>';
		$output .= $pad . $cat_name;

		if ( $args['show_count'] ) {
			$output .= '&nbsp;&nbsp;(' . number_format_i18n( $category->count ) . ')';
		}

		$output .= "</option>\n";
	}
}

/**
 * @param $args
 *
 * @return mixed|void
 */
function ywp_dropdown_categories( $args = '' ) {
	$defaults = array(
		'show_option_all'   => '',
		'show_option_none'  => '',
		'orderby'           => 'id',
		'order'             => 'ASC',
		'show_count'        => 0,
		'hide_empty'        => 1,
		'child_of'          => 0,
		'exclude'           => '',
		'echo'              => 1,
		'selected'          => 0,
		'hierarchical'      => 0,
		'name'              => 'cat',
		'id'                => '',
		'class'             => 'postform',
		'depth'             => 0,
		'tab_index'         => 0,
		'taxonomy'          => 'category',
		'hide_if_empty'     => false,
		'option_none_value' => -1,
		'value_field'       => 'term_id',
		'required'          => false,
		'multiple'=>false,
	);

	$defaults['selected'] = ( is_category() ) ? get_query_var( 'cat' ) : 0;

	// Back compat.
	if ( isset( $args['type'] ) && 'link' === $args['type'] ) {
		_deprecated_argument(
			__FUNCTION__,
			'3.0.0',
			sprintf(
			/* translators: 1: "type => link", 2: "taxonomy => link_category" */
				__( '%1$s is deprecated. Use %2$s instead.' ),
				'<code>type => link</code>',
				'<code>taxonomy => link_category</code>'
			)
		);
		$args['taxonomy'] = 'link_category';
	}

	// Parse incoming $args into an array and merge it with $defaults.
	$parsed_args = wp_parse_args( $args, $defaults );

	$option_none_value = $parsed_args['option_none_value'];

	if ( ! isset( $parsed_args['pad_counts'] ) && $parsed_args['show_count'] && $parsed_args['hierarchical'] ) {
		$parsed_args['pad_counts'] = true;
	}

	$tab_index = $parsed_args['tab_index'];

	$tab_index_attribute = '';
	if ( (int) $tab_index > 0 ) {
		$tab_index_attribute = " tabindex=\"$tab_index\"";
	}

	// Avoid clashes with the 'name' param of get_terms().
	$get_terms_args = $parsed_args;
	unset( $get_terms_args['name'] );
	$categories = get_terms( $get_terms_args );

	$name     = esc_attr( $parsed_args['name'] );
	$class    = esc_attr( $parsed_args['class'] );
	$id       = $parsed_args['id'] ? esc_attr( $parsed_args['id'] ) : $name;
	$required = $parsed_args['required'] ? 'required' : '';
	$multiple = $parsed_args['multiple'] ? 'multiple' : '';

	if ( ! $parsed_args['hide_if_empty'] || ! empty( $categories ) ) {
		$output = "<select $multiple $required name='$name' id='$id' class='$class' $tab_index_attribute>\n";
	} else {
		$output = '';
	}
	if ( empty( $categories ) && ! $parsed_args['hide_if_empty'] && ! empty( $parsed_args['show_option_none'] ) ) {

		/**
		 * Filters a taxonomy drop-down display element.
		 *
		 * A variety of taxonomy drop-down display elements can be modified
		 * just prior to display via this filter. Filterable arguments include
		 * 'show_option_none', 'show_option_all', and various forms of the
		 * term name.
		 *
		 * @since 1.2.0
		 *
		 * @see wp_dropdown_categories()
		 *
		 * @param string       $element  Category name.
		 * @param WP_Term|null $category The category object, or null if there's no corresponding category.
		 */
		$show_option_none = apply_filters( 'list_cats', $parsed_args['show_option_none'], null );
		$output          .= "\t<option value='" . esc_attr( $option_none_value ) . "' selected='selected'>$show_option_none</option>\n";
	}

	if ( ! empty( $categories ) ) {

		if ( $parsed_args['show_option_all'] ) {

			/** This filter is documented in wp-includes/category-template.php */
			$show_option_all = apply_filters( 'list_cats', $parsed_args['show_option_all'], null );
			$selected        = ( '0' === (string) $parsed_args['selected'] ) ? " selected='selected'" : '';
			$output         .= "\t<option value='0'$selected>$show_option_all</option>\n";
		}

		if ( $parsed_args['show_option_none'] ) {

			/** This filter is documented in wp-includes/category-template.php */
			$show_option_none = apply_filters( 'list_cats', $parsed_args['show_option_none'], null );
			$selected         = selected( $option_none_value, $parsed_args['selected'], false );
			$output          .= "\t<option value='" . esc_attr( $option_none_value ) . "'$selected>$show_option_none</option>\n";
		}

		if ( $parsed_args['hierarchical'] ) {
			$depth = $parsed_args['depth'];  // Walk the full depth.
		} else {
			$depth = -1; // Flat.
		}
		$output .= walk_category_dropdown_tree( $categories, $depth, $parsed_args );
	}

	if ( ! $parsed_args['hide_if_empty'] || ! empty( $categories ) ) {
		$output .= "</select>\n";
	}

	/**
	 * Filters the taxonomy drop-down output.
	 *
	 * @since 2.1.0
	 *
	 * @param string $output      HTML output.
	 * @param array  $parsed_args Arguments used to build the drop-down.
	 */
	$output = apply_filters( 'wp_dropdown_cats', $output, $parsed_args );

	if ( $parsed_args['echo'] ) {
		echo $output;
	}

	return $output;
}

/**
 * How to use
 */
ywp_dropdown_categories(
	array(
        'orderby'           => 'name',
        'hide_empty'        => 0,
        'child_of'          => 0,
        'echo'              => 1,
        'multiple'          => true, // boolean. true for multiple items selection
        'selected'          => array( 23105, 23307 ), // Selected items as array
        'hierarchical'      => 1,
        'name'              => 'cat',
        'id'                => '',
        'class'             => 'postform',
        'depth'             => 0,
        'tab_index'         => 0,
        'taxonomy'          => 'product_cat',
        'hide_if_empty'     => false,
        'option_none_value' => - 1,
        'value_field'       => 'term_id',
        'required'          => false,
        'walker'            => new YWP_Walker_CategoryDropdown(),
    )
);