True. I think that a lot of people make the mistake of believing that there must be a one-to-one correspondence between personhood and nature. "Nature" simply means what a thing is. So billions of different people can share the same (human) nature.
It does not necessarily follow though that one person cannot have two natures. We may not see any examples in nature, aside from Christ, but we cannot conclude that this is necessarily impossible.
God is pure spirit (purely non-material) and pure actuality. He sustains all creatures in existence. It is certainly within his power to take on the nature of an infinitely inferior creature in addition to his own nature. Whether this has happened in history would only be knowable to us through divine revelation, as is in fact the case with Christ.
I was reading that Western Civilization's concept of personhood developed directly from the debates on Christ's person and nature. It's hard to wrap one's head around this, for instance that Taoist and Vedic thought, though they produced great civilizations, never produced the concept of the person which includes bodily integrity, psychological continuity and moral imputability.
It seems that they tend to shade off personhood into human collectivity on the one hand, and serial reincarnations on the other, concepts which inevitably result in an attenuated sense of individual human dignity and the rational soul.
I's like to look into this more, since I'm at the learning-the-alphabet level, just catching a limpse of it. It seems to impinge on the West's "Dialog of Civilizations" with, for instance, Islam --- too bad if we've shrugged off the truths of our own civilization!