first you need to add an event listener to the Event.COMPLETE as normal since it is going to be dispatched automatically and theres nothing you can do about it. Inside that event handler you can then dispatch your own custom even that the rest of the application listens for with your custom property attached to it. heres a quick example:

your event handling code would look like:

yourObject.addEventListener(Event.COMPLETE, function(event:Event):void{

  var myEvt:MyEvent = new MyEvent(MyEvent.COMPLETE, myCustomProperty);
  dispatchEvent( myEvt );

})

and the MyEvent class looks like:

package
{

  import flash.events.Event;

  public class MyEvent extends Event
  {

    public static const COMPLETE:String = "MyEventComplete";

    var myCustomProperty:*;

    public function MyCustomEvent(type:String, prop:*) :void
    {

      myCustomProperty = prop;

      super(type);
      // if you want your event to bubble 
      // be sure to specify : super(type, true)
    }

   //override clone() so your event bubbles correctly
   public override function clone() :MyEvent {

     return new MyEvent(this.type, this.myCustomProperty)

   }
  }
}

you can now add event listeners for your custom event just like any other event:

addEventListener(MyCustomEvent.COMPLETE, someFunction);

I m not an expert, but the following is working for me. (Names changed to protect the innocent).

Here is one of my custom events:

import flash.events.Event;
public class SomethingHappenedEvent extends Event {
    public static const SOMETHING_COMPLETE:String = "PictureTakenComplete";
    public var passedValue:int;

    public function SomethingHappenedEvent(i:int) {
        passedValue = i;
        super(SOMETHING_COMPLETE);      
    }
}

I have a listener set up to listen for my custom event. When the custom event fires, my doSomething() function is executed. Here s how I set that up:

mySecret.addEventListener(SomethingHappenedEvent.SOMETHING_COMPLETE,doSomething);

Inside the doSomething() function I have access to event s passedValue parameter:

private function doSomething(e:SomethingHappenedEvent):void {
    trace("did something: " + e.passedValue);
}

Finally, here is how I dispatch a custom event elsewhere in the code, passing in a parameter:

this.dispatchEvent(new SomethingHappenedEvent(myCounter));

1. Create Custom Event with data parameter
2. Your class ( (for example MyObject) should catch Event.COMPLETE using addEventListener and dispatch your custom event MyCustomEvent with your data in it
3. Catch your MyCustomEvent somewhere else (for example in MyAnotherObject)

MyCustomEvent.as

package
{
 import flash.events.Event;

 public class MyCustomEvent extends Event
 {
  public static const MY_CUSTOM_EVENT_COMPLETE:String = "myCustomEventComplete";

  public var data:Object;

  // Constructor
  public function CaretEvent(type:String, data:Object, bubbles:Boolean=false, cancelable:Boolean=false)
  {
   super(type, true, cancelable);

   this.data = data;
  }

  // Public Methods
  public override function clone():MyCustomEvent
  {
   return new MyCustomEvent(type, data, bubbles, cancelable);
  }
 }
}

MyObject.as

package
{
 import flash.events.EventDispatcher;
 import flash.events.Event;

 public class MyObject extends EventDispatcher
 {
  // Contructor
  public function MyObject()
  {
   addEventListener(Event.COMPLETE, onComplete)
  }

  // Private Methods
  private function onComplete(event:Event):void
  {
   dispatchEvent(new MyCustomEvent(MyCustomEvent.MY_CUSTOM_EVENT_COMPLETE, "This is my custom data"));
  }
 }
}

MyAnotherObject.as

package
{
 import flash.events.Event;
 import flash.events.EventDispatcher;

 public class MyAnotherObject extends EventDispatcher
 {
  // Constructor
  public function MyAnotherObject()
  {
   addEventListener(MyCustomEvent.MY_CUSTOM_EVENT_COMPLETE, onMyCustomEventComplete)
  }

  // Private Methods
  private function onMyCustomEventComplete(event:MyCustomEvent):void
  {
   trace(event.data);
  }
 }
}

Could you post some code so we can see how you are approaching this?

However I would highly recommend reading the flex live docs on creating and using custom events.

Here is a simple custom event based application, Take a look at the source, it might be what you are looking for.

I usually do something like this, maybe not the best approach, but you should know this way is available...

myObj.addEventListener("creationComplete", function(e:Event):void{otherFunction(e, "another Arg")});

From the sound of things, you may not need to extend FileReference, Event.COMPLETE, etc. if all you need is another property... will the following work for your purposes? If not, show me some code so we can be on the same page.

public function go():void {
    var downloadURL:URLRequest = new URLRequest("http://example.com/big.jpg");
    var otherParam:String = "another param";
    var fileRef:FileReference = new FileReference();
    fileRef.addEventListener(Event.COMPLETE, function(e:Event):void {
                                                handleLoad(e,otherParam); });
    fileRef.download(downloadURL);
}

public function handleLoad(e:Event,whatelse:String):void {
    Alert.show("we just loaded " + e.target + " with param " + whatelse);
}

That will get an extra parameter (whatelse) into the handleLoad() function that does the work. Or are you saying that at the time of the download you don t have the additional parameter?