Actually, I tend to agree with LM on this particular point, and it comes right back to the difference between 'scientific evidence' vs. 'empirical evidence'.
"Science", and specifically the scientific method can explore the "supernatural" in terms of it's effect on the physical universe. For instance, the whole concept of dark energy is postulated based upon the presumed effect of said invisible agent upon the process/speed of "space expansion" (another supernatural concept/agent by the way). There is no empirical evidence that "dark energy" has any physical empirical effect on a photon. The whole concept of dark energy is actually a supernatural agent/construct, that is built upon another supernatural agent/construct because "space expansion" has also never been demonstrated to have any net effect on any photon, in any lab.
You "might" be correct that "empirical physics" may be limited to studying the "natural realm", but even the empirical method has some ability to delve into cause/effect relationships in some instances.
If the supernatural agent in question cannot be controlled in experimentation, the empirical method may become limited, but not "science", or the scientific method. "Scientific evidence" isn't technically limited to demonstrated or to demonstrating cause/effect relationships in controlled experiments. If it were, Lambda-CDM could not and would not survive since it's built upon no less than four supernatural agents/constructs, none of which enjoy any cause/effect support in a lab in controlled experimentation.
String theory is another example where theoretical physics meets supernatural agents that include extra spacetime dimensions.
I'd have to agree with LM that science can indeed study supernatural agents based upon their net effect on the natural world.
The danger of course is that such supernatural agents may or may not exist in nature. In other words, like 'dark energy' theory which was built upon a premise that may or may not be true, it too may or may not exist based upon the validity of the original premise, or premises in this case.
Empirical physics allows us to delve into the cause/effect relationships in controlled experimentation. That's an optimal sort of evidence, but it's not a requirement in science, and in some areas of physics it's quite rare. Only 5 percent of current Big Bang theory enjoys empirical cause/effect support in the lab. The vast majority of the theory is based upon supernatural agents, and evidence that is 'scientific' to a degree (but quite dated today), but the cause/effect relationships are all assumed, they are not demonstrated empirically.