What you are doing here is denying any assumptions while making a major one in the same sentence. Methodolgies cannot be employed without subjective, philosophical underpinnings. Undertaking science with the assumption that only natural phenomena can be considered or observed is undertaking science with a particular philosophical point of view. It is a choice you and other observers have made from your own experiences. It is a stance incapable of objective, emprical testing in and of itself.
You are mistaking the definition of science with its methodology. Reaching conclusions based only on natural phenomena and the facts of the natural world is what science does; it's what science is. It is oxymoronic to say that one can do "science" but consider supernatural elements.
You can reach conclusions by including supernatural elements in your reasoning process, but you are not doing science. You are doing something else; theology, probably.
The methodology of science has been, over the last 500 years or so, so effective in producing tangible results that it has developed a cache of a type that it appears that any statement of fact must at least attempt to disguise itself as science or risk losing credibility with the public. But calling non-science "science" doesn't make it science. (You can call a "tail" a "leg", but that doesn't mean that dogs have five legs.)