perfect constructions - What role does this past-participle take?

Someone standing outside the Great Hall might well have thought some sort of explosion had taken place, so loud was the noise that erupted from the Gryffindor table. Harry, Ron, and Hermione stood up to yell and cheer as Neville, white with shock, disappeared under a pile of people hugging him. He had never won so much as a point for Gryffindor before. Harry, still cheering, nudged Ron in the ribs and pointed at Malfoy,who couldn’t have looked more stunned and horrified if he’d just had the Body-Bind Curse put on him. (Harry Potter and the Sorcerer's Stone)

I don’t find the same syntactic example as the highlighted case in OALD. Is it a certain type of have-structure that I don’t find yet. Or does the phrase, put on him, modify the previous noun phrase, the Body-Bind Curse?

Answer

This is an instance of HAVE employed in a resultative sense—it’s the sense at OALD 22:

22 (used with a past participle) have something done to suffer the effects of what somebody else does to you
She had her bag stolen.

The use is actually broader than OALD suggests; it as also employed to express positive results:

Now that we have that settled we can move on to the next item.

This use goes all the way back to Old English, and was in fact the ancestor of the Perfect constructions which emerged in Middle English. In Old English the underlying syntax at that time was HAVE + [Direct Object] + [PaPpl], with the PaPpl modifying the Direct Object. (We know this because nouns and adjectives had case endings in OE, and in this construction the PaPpl 'agrees' with the Direct Object). In Modern English, however, it is probably best understood as a reduced subordinate clause:

He had [ [that] a curse [was] put on him. ]

I advance this parsing because in ModE there is also a use with a bare infinitive instead of a past participle; this is employed when the verb in question may be used both transitively and intransitively and the participle would be ambiguous:

She had her house burn down. ... which may be similarly parsed as She had [that] her house burned down.

Using active burn instead of passive burned here prevents this being parsed as transitive burned down used with causative HAVE, as in OALD's 23:

23 (used with a past participle) have something done to cause something to be done for you by somebody else
You've had your hair cut!
We're having our car repaired.

This use also supports use with an explicit subject, OALD's #24:

24 to tell or arrange for somebody to do something for you
• have somebody do something He had the bouncers throw them out of the club.