Double negatives

In standard English it is perfectly possible to have two negative words in one sentence. This effectively gives the sentence a positive meaning:

• I didn't not do my homework.

This is the kind of sentence we might say after somebody claimed that we didn't do our homework. The example means:

• The claim that I did not do my homework is wrong.

In other words it means:

• I did do my home work.

Not only ... but also

The phrase:

• Not only A but also B

Means something like:

• A, and furthermore, B.

So:

• Not only did I do my homework, I also got an A for it.

means:

• I did my homework and, furthermore, I got an A for it.

Using "not only" with negative clauses:

Not only are all humans not equally intelligent, but those who are truly intelligent are also not equally as intelligent in every field.

We can paraphrase this sentence using furthermore:

• All humans are not equally intelligent, and furthermore, those who are truly intelligent are not equally as intelligent in every field.

Both of the sentences above are perfectly grammatical. We could also use the Original Poster's rephrasing here:

• All humans are not only not equally intelligent, but those who are truly intelligent are also not equally as intelligent in every field.

This sentence is perfectly grammatical too. (It's a bit difficult to read though.)

^{Grammar note:}

^{... nor [those who are truly intelligent] are equally intelligent. (ungrammatical)}

^{Notice that the example above is ungrammatical. The Subject of the clause is those who are truly intelligent. In the example it occurs before the auxiliary verb are. However, the example has a negating word at the beginning of the clause, the word nor. When this happens we must use Subject auxiliary inversion. We need to put the Subject after the auxiliary verb like this:}

^{- nor are [those who are truly intelligent] equally intelligent.}