You can certainly change the style of the check-box, but it won't work like that. It will be first click Check (and now you change the style, let's say), second click un-checked, third click Cross (again you can change the style, if you wish), fourth click un-checked, etc.
If you want a tri-state box then you're better off using a button instead of a check-box.
Thanks for your reply.
How to do it using button?