MagentoCoreJsOverwrite.js

<script type="text/javascript">
// Extend original Billing class and overwrite newAddress method
var BillingCustom = new Class.create(Billing, {
  
  //$super represents the original function
  newAddress: function($super, isNew) {
    $super(isNew); // call original function.  You don't have to call the original function you may or may not want to.  You might just copy the original function and adapt it.
    // Do something else here after calling the original function
  }

});
//Replace new Billing() with new BillingCustom()
//var billing = new Billing();
var billing = new BillingCustom();

//Extend payment class and overwrite beforeValidate function
var PaymentCustom = new Class.create(Payment, {
  beforeValidate : function($super) {
    var original_result = $super();
    //do something else to original_result
    return original_result;
  }
});

var payment = new PaymentCustom('checkout-payment-method-load', '<?php echo $this->getUrl('checkout/onepage/savePayment') ?>');
payment.currentMethod = "<?php echo $this->getQuote()->getPayment()->getMethod() ?>";
</script>