I have a textbook for a course on Japanese pedagogy, and one of the sections is about sentence structure. It talks about how adjectives in Japanese have some characteristics that in English only verbs have. For example, Japanese adjectives can sometimes take two or three arguments. One example is　ほしい, and it gives this example sentence for its use with three arguments:

私はその人を秘書に欲しい。
'I want that person as (my) secretary.'

I'm a bit confused by the phenomenon, mostly because I always think of を as being used only with verbs, and even then only with volitional verbs.

The book mentions that a sentence like this is wrong:
私はお金を欲しい。
Of course, が should be used here, which is completely in line with how I normally think が and を are used.

So, my question is, can anybody else think of other situations in which を can be used in sentence without a volitional verb (i.e., a verb you can choose whether or not to do)? Or does anybody have any insightful information on why を can be used in this kind of example?

It depends on how prescriptive you want to be. を is used by native speakers with 好き and 嫌い, as well as potential forms, できる, わかる, and some other things as well.

I think that を's association with volition causes native speakers to use it in some situations where they feel like some sort of volition is involved even if the predicate isn't technically volitional. In the case of ほしい, you can see how some people might feel like there's a certain level of volition involved (whereas the prescriptive requirement for が says that you can't choose what you want).

(Of course, the main difference between what is normally called an "i-adjective" and an English adjective is that the Japanese "i-adjective" does not require a copula; it can stand on its own as a predicate.)

IMHO, with the first sentence, I think there is some implied meaning.

I think 秘書に欲しい is just a shortened version of:

秘書になって欲しい
OR
秘書にして欲しい

The second sentence is wrong because お金を欲しい should be お金が欲しい.
Watch j-drama enough times and you'll eventually hear someone say お金が欲しい....

Although "I want him as my assistant" isn't identical to "I want him to become my assistant".

As yddt mentioned, を　it isn't wrong, it's just not taught as standard.
eg 金を欲しいと言ったので少しやった. (kenkyuusha dict)

There are all good thoughts on the matter, but I wonder if there are any other examples which are considered more standard. The guy who's writing seems pretty on the ball (Stefan Kaiser, a linguist).

He talks as if
「私はその人を秘書に欲しい。」
is standard literary Japanese, whereas,
「私はお金を欲しい。」
would be considerd incorrect. And,
「魚を好きだ。」
Is substandard, but not exactly incorrect.

So, I guess I'm wondering about other situations in which を is used without a volitional verb that would be considered standard enough to publish in something like a newspaper. He makes it sound like it would be standard with any adjective that has three arguments (in this case, one person, another thing/person, and one more thing/person). But are there actually any examples of that besides 欲しい?