What makes a haecceity unrepeatable?

My question is this: what is it about a thisness (haecceity) that makes it so unrepeatable? Take Socrateity. Why couldn't God create another one, an identical copy or clone?

As far as I can tell, if we assume that God is omnipotent (by which I mean that God can bring about anything that does not involve a contradiction), then the only way that a thisness could not be cloned is if doing so brought about a contradiction.

Suppose, for instance, that we assume (as some modern metaphysicians do) that a thisness is the property of being identical to oneself. In that case, Socrateity would be the property of being identical to Socrates. Now suppose that God created a clone of Socrates, and cloned his Socrateity as well. Let's call this clone 'Harold', and let's call the Socrateity-clone 'Haroldeity'.

Since Haroldeity is a clone of Socrateity, it would be the property of being identical to Socrates. Thus, Harold would be identical to Socrates. But Harold is not identical to Socrates. On the contrary, he is just a clone of Socrates. Thus, Harold would turn out to both be identical to and non-identical to Socrates, and that's a contradiction. So God could not clone Socrateity if it amounted to being identical to Socrates, for cloning that property would result in a contradiction.

One might take this example and generalize: the only way that cloning a thisness will result in a contradiction is if the thisness involves some sort of intrinsic reference to the individual in question. For ultimately, the contradiction is going to involve being identical to vs. not being identical to the individual in question. (It would be irrelevant if the resulting contradiction amounted to being identical and not being identical to Beulah the cow. We're talking about Socrates here, so the contradiction is going to have to pertain to him.)

So, one might think, if a thisness lacks any sort of reference to the individual in question, then it could be cloned after all.