As the other stated, you can't. Although has H2CO3 pointed out, you can use associative references. On Apple Documents:
Note that a category can’t declare additional instance variables for
the class; it includes only methods. However, all instance variables
within the scope of the class are also within the scope of the
category. That includes all instance variables declared by the class,
even ones declared @private.
If you want to go for associated object, you can use this answer. Moreover, you can use this post by Ole Begemann.
