How can I go about making a child class override a privileged method of a base class?

If its not possible, is there another way to achieve what I am trying to accomplish in the simple code example below?

I cannot convert the baseclass function parseXML() to public because it requires access to private variables

    function BaseClass()

    {

        var map = {};



        // I cannot make this function public BECAUSE it accesses & changes private variables

        this.parseXML = function( key, value )

        {

            alert(BaseClass::parseXML());

            map[key] = value;

        }

    }



    function ChildClass()

    {

        BaseClass.call(this);

        this.parseXML = function( key, value, otherData )

        {

            alert(ChildClass()::parseXML());



            // How can I call the base class function parseXML()?

            //this.parseXML();  // calls this function not the parent function

            //MyClass.prototype.doStuff.call

            BaseClass.prototype.parseXML.call(this, key, value);  // fails

            //BaseClass.prototype.parseXML(); // fails



            // perform specialised actions here with otherData

        }

    }



    ChildClass.prototype = new BaseClass;



    var a = new ChildClass();

    a.parseXML();