It happened to me to think about this (but from another perspective). It seems to me that the sentences "I want [A]", where A is an object outside me, and "I want [to want A]" are essentially different. But the sentences "I want [to want A]" and "I want [to want to want A]" are not really different since both have as object my own will. Or said in another way: wanting to want something is already wanting something.

Moreover an essential differentiation that is not addressed is the difference between desire and will (not easy).