Wikipedia’s article on Osama bin Laden’s compound in Abbottabad, Pakistan quotes “US officials” describing it as “extraordinarily unique”.
Some style guides advise or prescribe against any modification of unique. Either something is the only one of its kind, or it’s not. It can’t be (for example) very unique. While modifying unique is probably best avoided in formal contexts, there can be no doubt that many people say or write it informally and normally. Google Ngram Viewer shows not (by far the most common), very, as, most, so, quite, rather, somewhat, almost and probably unique. Some of these are (probably) more acceptable, and others less so.
Extraordinarily unique isn’t on Ngrams’ top 10 results (its usage is about one-tenth that of probably unique), but a general Google search shows about 391,000 results, starting with blind auditions on The Voice, the Atlanta Motor Speedway and the Villa Bismarck on Capri.
It might just be possible to describe something as extraordinarily unique if it’s extraordinary as well as unique – a whole level more unique than anything else. Australia has many unique animals, but the platypus is extraordinary. Anyone familiar with jerboas will accept the kangaroo, but when the first samples of dead platypuses (?platypi, ??platypodes) arrived in England, the experts there thought someone here was playing a practical joke on them. But “except for its size and exaggerated security measures,” Bin Laden’s compound “itself did not stand out architecturally from others in the neighbourhood.”
Never Pure and Rarely Simple 
I don’t necessarily believe that something can’t be “more unique” than another thing. If uniqueness, or one-of-a-kind-ness, can be evaluated by the degree to which something is not of the same kind or style as another thing, then that degree of unsameness can be described; therefore some things can be more unique than others, and even extraordinarily unique. After all, how we categorize objects into different boxes is ultimately somewhat arbitrary and based on various subjective criteria.
And why does no one call out the Preamble to the USA Constitution for its use of “more perfect”?
On the subject of pluralizing the platypus, John Oliver may have the definitive statement (but for the case of the not-very-humble octopus) here:
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Dictionary.com’s usage note mentions ‘“absolute” words as complete, equal, perfect, and especially unique’. Its definition includes ‘not typical; unusual’. A platypus is definitely very not typical or unusual. Its definition for ‘perfect’, on the other hand, doesn’t seem to have any ‘less-than-absolute’ definitions.
Platypus simply isn’t a Greek word – it’s an English word made up of Greek bits, so it can (and probably must) follow English pluralisation. But even though octopus is an original Greek word, it doesn’t necessarily have to follow the original Greek pluralisation. Not all English words of Greek origin do. I’ll stick with octopuses.
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Surely some things are more “unusual” than others? Ah, the dictionary.com definition of “unique” you referred to (#5) gives an example that contains the phrase “very unique,” which is not compatible with absolutism.
And George Orwell might disagree with “equal” being absolute, at least for animals. But that, of course, was for ironic effect.
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I am in two minds about this. I generally like the idea of words having one meaning and meanings have one word, so that we can say what we mean and mean what we say, but I know that language doesn’t/languages don’t work like that. Variety and change gives us subtlety, poetry and humour, as well as plausible deniability, misuse and abuse of language (and power – pace Orwell).
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On the topic of “equal”, a current hot sociopolitical topic here in the US, the anti-racism movement, involves (among other things) the words “equality” and “equity.” As is not pointed out enough, these have different connotations: in brief, equality refers to opportunity while equity refers to outcome.
The programming language Lisp has at least four different functions to compare objects in terms of equality: “eq”, “eql”, “equal”, and “equalp”. Briefly, there are different degrees of sameness: whether two objects are actually the same object (occupying the same address in memory), whether they are not “the same” but identical in bitwise content, or (since Lisp is a list processing language) whether they are two distinct lists that happen to contain elements that are respectively equal to one another in one of the above senses. As you can see, it gets complicated
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