You might find this interesting: 11 Universities with Paranormal Studies [destinationamerica.com]

I know Stanford is the oldest, and they did work with the CIA on MK Ultra.

Here is a just a hint of what they are about. If you are more into what "may" be than what is, It may appeal to you. I looked into them in the early eighties. Not much for science really.

Noetic science is an "exploration into the nature and potentials of consciousness using multiple ways of knowing—including intuition, feeling, reason, and the senses" according to its promoters. Aka, a form of bullshit, most famously promoted by Dan Brown in The Lost Symbol.

Note that noetic "science" and noetic philosophy are distinct. Noetic (from the Greek noetikos, "mental" ) philosophy is philosophy dealing with the mind, intellect, or consciousness. However, this more often goes under the more obvious name of "theory" or "philosophy of mind" these days. Noetic "science" is closer to the pseudoscience of parapsychology and other such New Age fluff as "expanding your consciousness."

Institute of Noetic Sciences[edit]
The Institute of Noetic Sciences is the primary outlet for this form of woo. It was co-founded by former astronaut Edgar Mitchell and former Exxon executive and crank billionaire Paul N. Temple, who is also associated with the fundamentalist Christian organization The Family,

According to the Institute, the core of Noetic Science is as follows:

“”Noetic sciences are explorations into the nature and potentials of consciousness using multiple ways of knowing—including intuition, feeling, reason, and the senses. Noetic sciences explore the "inner cosmos" of the mind (consciousness, soul, spirit) and how it relates to the "outer cosmos" of the physical world.[1]
All of which sounds more like other ways of knowing than science.

Unsurprisingly, noetic science has come under criticism from skeptics and actual scientists, and the organization Quackwatch has placed the Institute of Noetic Science on the "questionable organizations" list.
[rationalwiki.org]

I would be surprised if there were many. I would actually be surprised if there were any.
Research costs money. Those researchers do not get payed much, but still. Often they need a lab. And heating in the winter. So most sources of grant money have to decide on what kind of research would make that money well spent.
Sure, it may be practical in the discussion with some loonies if there was a long list of scientific papers each debunking, scientifically, another crazy belief about something supernatural. But those researchers could also spend their time researching something that gives actual insight and tells us something we do not already know. Also, the loonies tend to stick to their beliefs anyway, no matter how many scientific articles we point out to them.
So unless some eccentric billionaire tries to get rid of their money that way, I'd say the chances are slim.

No.

[psychologytoday.com]

Physics, Math, and Chemistry are sciences. Usually areas that feel the need to attach science after their name are pseudosciences...

James Randi has offered 1 million dollars to anyone who can prove the supernatural. no one has claime the prize yet

Read up on the work of Michel Persinger and the shaki helmet experiments.

Many phenomena, such as orbs, are classified "false unknown" which means that rather than a single unexplained phenomenon they are in fact a complex of several explained phenomena.

A sociologist at my university wanted to start a parapsychology group, starting with a focus on electronic voice phenomenon. He had a set of experiments conducted by lay persons that he wanted to follow up on but once the faults in those experiments were explained to him he dropped the idea. I suspect that sort of thing tends to be how serious attempts to study the paranormal end.

What is a woo event? Have not heard that term used this way before?

This is a list of cryptozoology groups. Credible organizations? I would doubt it.
[newanimal.org]

SETI: search for extraterrestrial intelligence--kind of woo...