Generally, I think the term "double fulfilment" is a bad choice. Here's why: it is open to all kinds of abuse, some types of which have been mentioned.
Instead, I think that with regard to Christ, we should see the OT chock full of typological references that have a "perfect" fulfilment in Christ. It isn't that Solomon doesn't fulfill David's son, its just that he can only BE an imperfect fulfillment. Jesus, after all, never has to address that part "if he commit iniquity..." A perfect Son doesn't sin at all. So, Solomon, the sinner, cannot exhaust the prophecy, or be an ideal son. There Solomon himself must not only fulfill the prophecy on one level, but IS himself a kind of prophetic promise that someone Better is coming.
So, if Solomon IS a kind of prophesy of Jesus, then everything that pertains to Solomon--including the prophecy regarding Solomon--must in some way point through Solomon to Jesus.
Then, there are prophecies that seem to build, or have "intermediate" fulfilment. Judgments of all kinds serve as these, as well as Blessings. There is a sense in which everything prophetic is eschatological. Everything points to an ideal end-state or context, in which all matters of consequence are settled. Every earthly judgment in proleptic, in that it points to a final crisis. When the Lord says, "Once more, and I will shake..." (Hag. 2:6-7; Heb. 12:27), speaking of the setting up of the everlasting kingdom, we recognize that this is an "already-not yet" kind of prophecy. It has a definitive fulfilment (ONCE more) in the ministry of Jesus--AND, it has a consummative fulfilment, in the arrival of the age to come.
Instead of "double-fulfilment: (or triple, etc.), we might do better thinking of such fulfilments as successive wavelets hitting the beach, or as ripples in the pond, or maybe as "nested". Our perspective on the events shifts, or rather, the events themselves may be small, or great, or they may be monumental. And if we were to be lifted up to God's perspective (as the prophets were) we would understand al little better what they were trying to convey (for surely, God's perspective overwhelms the man). The "true" fulfilment is that which completes.
Here might be a good place to revisit the "prophetic perspective." Some think of the prophet as a man who stands a bit higher than us, and has a telescope, but fundamentally stands on the same plane as us. Often this is presented as the "two mountain ranges" analogy. The prophet can't tell that the far range is actually farther away, and much higher.
I think that's totally erroneous.
The prophet is not "on our plane, only enhanced to see beyond us." He is "one of us," yes, but he has been removed from us and taken to Heaven ("...in a vision, in a dream," or "whether in the body, I cannot tell; or whether out of the body..."). Remember Micaiah? "And he said, Hear thou therefore the word of the LORD: I saw the LORD sitting on his throne, and all the host of heaven standing by him on his right hand and on his left" (1 Ki. 22:19). How about Elijah, who fled to Horeb, only to find that heaven settles on the mountainside, and he is called to a meeting?
And the prophet sees things as God sees them and he is sent back to tell us (!) what he's seen. He speaks the Words he has been given by God, and he searches them himself, to try and fathom their full meaning (1 Pet. 1:11f). And we wonder why "And I, Daniel, was overcome and lay sick for some days. Then I rose and went about the king's business, but I was appalled by the vision and did not understand it" (Dan. 8:27)? Or Isaiah's "undone" condition? The miracle was surviving the vision!
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Rev. Bruce G. Buchanan