Continuing on with the the discussion about hard and soft polytheism, I'd like to take a look at the theology of late classical paganism. This theology was derived from Neoplatonist philosophy, and was briefly declared the official religion of the Roman Empire under Julian the Apostate. If Julian's plan for a revived paganism with an organized hierarchy had taken root, this would probably be the dominant religion of the Western world.
In late pagan theology, there is no absolute distinction between polytheism and monotheism. Rather, the source of everything in existence is considered to be One, but the One manifests or emanates through multiple different gods. These gods are organized into a hierarchy depending on how close to the One they are.
The Hypercosmic Gods are closest to the One, followed by the Demiurge. The Demiurge is the creator of the world, and is roughly equivalent to the God of the Old Testament. Below the Demiurge are the Cosmic Gods, which are the gods of the classical mythologies. These gods definitely have distinct personalities in some sense, but they are also aspects of the One- because everything is.
This theology is distinctly similar to that of Hinduism, where the gods are simultaneously manifestations of an underlying unity and distinct pathways to that unity. If both classical paganism and Hinduism developed along those lines, I think a strong case can be made that this model is implicit in Indo-European religion. As such, the hard polytheist claim that the gods are not aspects of a greater unity is not supported by the evidence of ancient pagan religion.