Java SE (Java Platform, Standard Edition)

I'd like to create a JList where I can select multiple items as if the control key were down, but without having the control key down. I thought that perhaps I could do this by extending JList and overriding its processMouseEvent method, setting the MouseEvent object to think that control is pressed and then calling the super method like so, but it doesn't work (I still need to press the control key to get my desired effect):

import java.awt.Component;
import java.awt.event.InputEvent;
import java.awt.event.MouseEvent;

import javax.swing.*;

public class Ctrl_Down_JList {
  private static void createAndShowUI() {
    String[] items = {"Sun", "Mon", "Tues", "Wed", "Thurs", "Fri", "Sat"};
    
    JList myJList = new JList(items) {
      @Override
      protected void processMouseEvent(MouseEvent e) {
        
        // change the modifiers to believe that control key is down
        int modifiers = e.getModifiers() | InputEvent.CTRL_DOWN_MASK;
        
        // can I use this anywhere?  I don't see how to change the 
        // modifiersEx of the MouseEvent
        int modifiersEx = e.getModifiersEx() | InputEvent.CTRL_DOWN_MASK;
        
        MouseEvent myME = new MouseEvent(
            (Component) e.getSource(), 
            e.getID(), 
            e.getWhen(), 
            modifiers, // my changed modifier
            e.getX(), 
            e.getY(), 
            e.getXOnScreen(), 
            e.getYOnScreen(), 
            e.getClickCount(), 
            e.isPopupTrigger(), 
            e.getButton());
        super.processMouseEvent(myME);
      }
    };
    
    JFrame frame = new JFrame("Ctrl_Down_JList");
    frame.getContentPane().add(new JScrollPane(myJList));
    frame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
    frame.pack();
    frame.setLocationRelativeTo(null);
    frame.setVisible(true);
  }

  public static void main(String[] args) {
    java.awt.EventQueue.invokeLater(new Runnable() {
      public void run() {
        createAndShowUI();
      }
    });
  }
}

Any ideas would be much appreciated!