First, Radio Buttons work like the mechanical station selection buttons on a radio, you can only select one and that button can only be unselected by selecting another button.
You want to us check boxes as one can have multiple selections, unselect by clicking again, and can create exclusionary groups either by a field naming convention or using JavaScript.
You might want to experiment with the 2 types of buttons some with only one with the same name and others where multiple buttons or boxes share the same name and observe what happens.
