The verb "keep" can be used with a direct object and a prepositional phrase, as in the following sentence:
He kept a black book in his desk.
What is the grammatical role of the PP "in his desk"? Is it an adverbial adjunct, or is it a complement? (Or is it some third thing?) Semantically, it seems to describe the location of the direct object, so the meaning seems consistent with its being an "object complement". However, my first thought was that it was an adverbial adjunct.
I found a list of tests for finding out if something is an adjunct or a complement on the following page: "XBar Theory: Complements and adjuncts", Linguistics 522, Jean Mark Gawron, San Diego State University. But even after going through them, I'm not sure if "in his desk" is an adjunct or a complement here.
My attempt at applying the tests:
Order: an adjunct cannot come between a head and a complement. The examples are in noun phrases, not verb phrases. The direct object "a black book" is not an adjunct, so this test is not applicable to the original sentence. I guess the sentence could be altered to make the test applicable if I tried to add an adjunct before "in his desk":
Do-so replacement: "do so" can replace
V's (using the terminology of X-bar theory). I'm not sure whether "Dan kept a black book in his desk, and Sally did so in her bag" is ungrammatical: it sounds bad to me, but "Dan kept a black book, and Sally did so also" also sounds bad, and that second sentence doesn't even have any prepositional phrases involved.
Coordination: it's ungrammatical to coordinate a complement with an adjunct. "He kept a black book in his desk and despite my advice" doesn't seem right to me, but I'm not sure if this is strong evidence that "in his desk" is a complement.
Preposing: Apparently, "verbs dont like having their complement PPs preposed". This test seems to point towards "in his desk" being an adjunct, because "In his desk, he kept a black book" seems acceptable and grammatical to me.
Araucaria's answer to "Is this Adverbial a complement or an adjunct?" on ELU seems to say that an adverbial adjunct should be equally acceptable if a verb and direct object are replaced with "do it", giving the example "They played football in the park / They did it in the park". This suggests to me that "in his desk" is not an adjunct, because we can't say "He did it in his desk" to mean "He kept a black book in his desk".
Have I been interpreting these tests correctly? Are there any other tests I should be using?