Passing a callback function with included parameters?

I have this below code..

function getGrades(grading_company) {

    if (grading_company == 'Not Specified') {

        // Remove grades box & show condition box
        showConditionBox();

    } else {

        // Set file to get results from..
        var loadUrl = "ajax_files/get_grades.php";

        // Set data string
        var dataString = 'gc_id=' + grading_company;

        // Set the callback function to run on success
        var callback = showGradesBox;

        // Run the AJAX request
        runAjax(loadUrl, dataString, callback);  

    }

}

function runAjax(loadUrl, dataString, callback) {

    jQuery.ajax({
        type: 'GET',
        url: loadUrl,
        data: dataString,
        dataType: 'html',
        error: ajaxError,
        success: function(response) {
            callback(response);
        }
    });    

}

Edit: Here is the function that gets called as the callback function:

function showGradesBox(response) {

    // Load data into grade field
    jQuery('#grade').html(response);

    // Hide condition fields
    jQuery('#condition').hide();
    jQuery('#condition_text').hide();

    // Show grade fields
    jQuery('#grade_wrapper').show();
    jQuery('#grade_text_wrapper').show();    

}

Now if I wanted to pass the grading_company variable to the callback function as a parameter is there a way to do that without having to add it as another parameter in the runAjax call? I'm trying to keep the runAjax function open to other usage so I don't want to pass in any extra parameters; but if it can somehow be included within the callback then great.