A Guild of Wizard Pupils?

[Inziladun]

J.R.R.T somewhat addressed this:

A difference in the use of 'magic' in this story is that it is not to be come by by 'lore' or 'spells'; but is in an inherent power not possessed or attainable by Men as such.

The Letters of J.R.R. Tolkien #155.

That would certainly seem to indicate that 'wizardry', as it describes the innate supernatural abilities of the Istari (and Sauron) cannot be taught to lesser beings.
At first glimpse, that might seem to be at odds with ROTK: We see the Lord of the Nazgûl

Then the Black Captain rose in his stirrups and cried aloud in a dreadful voice, speaking in some forgotten tongue words of power and terror to rend both heart and stone,

And the Mouth of Sauron, as mentioned

He learned great sorcery, and knew much of the mind of Sauron; and he was more cruel than any orc.

I think all this can be reconciled by noting that both the Witch-king and the Mouth had completely surrendered their sense of being and wills to Sauron. As such, they were essentially merely instruments of his will. Perhaps that allowed them the use of powers beyond their normal means under certain circumstances.

The Elves, to a much lesser extent, also had powers that appeared to Men to be 'magical'. Those also were abilities derived from the nature of their being and could not be transferred to others.