multiple comment text areas

To add new fields, simply append them to the default fields with a plugin.

<?php
defined( 'ABSPATH' ) AND exit;
/* Plugin Name: (#85059) Append form fields to comment form */

add_filter( 'comment_form_default_fields', 'wpse85059_comment_form_extd', 100 );
function wpse85059_comment_form_extd( $fields )
{
    // Append new fields …
    if ( 'comment_form_default_fields' === current_filter() )
    {
        foreach ( array( 'ctax_1', 'ctax_2', 'ctax_3' ) as $ctax )
            $fields[] = "<input value="{$ctax}" name="{$ctax}" />";
        return $fields;
    }
}

Then there’s also the possibility to use comment meta data. More about it can be read in the Codex.

• add_comment_meta()
• get_comment_meta()

To attach the meta data, you can hook into an action:

add_filter( 'comment_id_fields', 'wpse85059_comment_meta_fields', 10, 3 );
function wpse85059_comment_meta_fields( $result, $id, $replytoid )
{
    add_action ( 'comment_post', 'wpse85059_comment_meta', 1 );

    foreach ( array( 'ctax_1', 'ctax_2', 'ctax_3' ) as $ctax )
        $result .= "<input value="{$ctax}" name="{$ctax}" />";

    return $result;
}
function wpse85059_comment_meta( $comment_id )
{
    // Only run once
    remove_filter( current_filter(), __FUNCTION__ );

    foreach ( array( 'ctax_1', 'ctax_2', 'ctax_3' ) as $ctax )
        add_comment_meta(
             $comment_id
            ,$ctax
            ,$_POST[ $ctax ]
            ,true
        );
}

Note: This is not tested, but should give you a starting point.