Based on a survey of approximately 1,000 professional philosophers in 99 philosophy departments of North America, Europe, and Australasia:
Conceivable but not metaphysically possible: 36 percent
Metaphysically possible: 23 percent
Inconceivable: 16 percent
Other: 25 percent
The “other” is taxing my imagination.
Source: David Chalmers and David Bourget, “What Do Philosophers Believe?,” Philosophical Studies, quoted in The Philosophers’ Magazine, 1st Quarter 2014