A society to promote the pursuit of science by the common man or woman, with rigorous debate and discussion. A society where everyone agreed on the ground rules about what constituted 'science' and what constituted quackery.
We are almost to the point where we have enough multi-billion individuals that such a society could be endowed to create a place for science and scientists. Research without the requirement to teach undergraduates, publication with the requirement of a Ph.D. I could imagine that people who could learn the discipline to do the research could be supported in that research by some facilities and a modest stipend. Not the crazy big investment stuff like Fusion Reactors, but smaller problems like characterizing digestive flora in developed and undeveloped countries.
Its probably a pipe dream. But I wish such a group existed.