I hold the view that the term "supernatural" is simply an incoherent concept. No one has been able to demonstrate that that the set of "supernatural" things is not empty, or how you would be able to tell! Still, if we presume that there is a coherent definition, and there is at least one thing in that set, and that one thing is a god which can interact with the world, then at least the effects should be testable.
I was thinking about this term "supernatural" recently, and it occurred to me that this term is really a label-of-the-gaps and, because the only denizen of the supernatural is purported to be God: the term "supernatural" is a mask for the God of the gaps. This came to me when I realized that the ancient Christians did not believe in the supernatural! Their cosmology was weird (by modern standards), where they imagined different materials - both earthly and heavenly. Thus, God was in what they would call the universe, but located within a divine part of the universe (somewhere within the Moon and the other planets). See a few ancient writings, like the Ascension of Isaiah, for a tour. One of the issues the Church had with Galileo was that, with his telescope, it became clear that the Moon looked just like an ordinary rock and not something perfect, made of divine materials.
Once we falsified the ancient cosmology, the "heavens" had to move somewhere else. Essentially, it has to move beyond where we can directly observe, which inconveniently for the theists, is nearly everywhere these days. Thus, the only place to go is the (undefined) region of the "supernatural". Notice that the influence of God has also followed this path, with the strongest arguments for God lurking in the ultimate origin of the universe (through the so-called fine-tuning of the physical constants), the origin of life (not the development of species, because once the first replicator is formed, evolution explains the resulting diversity), and ancient history (because modern history doesn't show the evidence of God's influence) - all out of reach of our current access to data.
So , when theists toss around the term "supernatural", we can recognize it for what it is - a simple statement of ignorance, and another facet of the God-of-the-Gaps.