It's late and my brain is contorting itself. Please bear with me.
This is the closest thing I've seen so far:
"The VERITAS Research Program of the Laboratory for Advances in Consciousness and Health (formerly the Human Energy Systems Laboratory) in the Department of Psychology at the University of Arizona was created primarily to test the hypothesis that the consciousness (or personality or identity) of a person survives physical death." From the website.
Dr. Gary E. Schwartz founded this lab, if memory serves. He's authored a few books on the subject.
Another is IONS (The Institute of Noetic Sciences).
I think Consciousness Studies is the field that is trying to approach the general subject area from a scientific perspective. As far as I can tell it's still on the fringe.
As I understand things, and I'm not a scientist, science is five-sensory. Multisensory perception is beyond its domain and capabilities. Since there's a requirement that something (here an experience) be observable, repeatable and then subject to peer review, I don't think we'll get anywhere using the scientific method as our means and standard of proof. That science has made great progress for all of us in the physical domain is to be respected, but in modern times it has asserted itself as the arbiter of secular (or all) truth, or at least that's the status that people have given it. Such authority as it seems to extend to things beyond the five senses is, I think, beyond its mandate and no longer pure science as I understand it, but "scientism," a belief system in itself.
As we are dealing with experiences that are radically subjective, proof must be had on that basis, subjectively. Using your reason and through repeated experiences of the same kind, along with partnering with others whenever possible, should prove to you that your experiences are real (or not). This is empirical in the philosophical sense, if not strictly scientific, and is the best any of us can do for now.
From Wikipedia:
"In philosophy, empiricism is a theory of knowledge that asserts that knowledge arises from evidence gathered via sense experience. Empiricism is one of several competing views that predominate in the study of human knowledge, known as epistemology. Empiricism emphasizes the role of experience and evidence, especially sensory perception, in the formation of ideas, over the notion of innate ideas or tradition.
In a related sense, empiricism in the philosophy of science emphasizes those aspects of scientific knowledge that are closely related to evidence, especially as discovered in experiments. It is a fundamental part of the scientific method that all hypotheses and theories must be tested against observations of the natural world, rather than resting solely on a priori reasoning, intuition, or revelation. Hence, science is considered to be methodologically empirical in nature."
Again, note the emphasis on sensory experience, which means five-sensory, not multisensory. If we substitute multisensory for five-sensory, then i think our approach through experience and observation is empirical. I think TMI and Bruce have proven that such experiences are repeatable. But for now our proof is subjective and inter-subjective, and that's the best we can expect.
Hope this helps!
Rob