Custom Ajax Response Methods

Custom Ajax Response Methods

Hi,
I was wondering if there is a way to implement a custom Ajax response method, besides what's already there, like "done" or "fail".
For example: 
  
// Assign handlers immediately after making the request,
// and remember the jqXHR object for this request
var jqxhr = $.ajax( "example.php" )
.done(function() {
alert( "success" );
})
.fail(function() {
alert( "error" );
})   .MyCustom(function() {
     
alert( "Item Already Exists In the List" );
})
.always(function() {
alert( "complete" );
});
}