I have a new, mirrorless, interchangeable lens, tilt-shift (MILTS) camera. My MILTS camera allows any lens with a Canon EF mount to be shifted by 15 mm and tilted by 10° in any direction (tilt and shift movements are perpendicular to each other). In my case, the camera's specifications are identical to a Sony A7r, but it could just as well be any Sony E mount camera; thanks to the Canon EF - Sony E mount tilt-shift adapter from Mirex (it is not advertised on their website - you have to contact the company by e-mail).
The Sony E mount tilt-shift adapter's specifications are virtually identical to the version for micro four thirds (M4/3) cameras. The tripod mount is interchangeable between the two adapters and the tilt-shift mechanisms are the same; only the lever to rotate the adapter is differently designed. I find it more convenient on the Sony model. First, I had planned to use my micro four thirds tilt-shift adapter with a cheap M4/3 - Sony E mount adapter, but unfortunately the two adapters that I have tried were not fitting properly. Albeit not fitting well at all, the set-up allowed to test my manual lenses and their tilt-shift capabilities on a full frame body. To my surprise, all the nice, old lenses that I am using allow both, tilt and shift movements, although not the full amount. As expected, the corners of the frame get black when the lens is shifted maximally. The exact degree of tilt and shift (without vignetting) is specific for each lens (due to different image circles) and also depends on the sensor size of the camera (it would be much less of an issue with a smaller sensor).
All in all, I am just as satisfied with the Sony version of the tilt-shift adapter as with my micro four thirds model. If at all, handling is even easier on the Sony body, because it is slightly larger than my Lumix GH1 and because of focus peeking: It is quite cool to see colors indicating the areas in focus move across the frame as you tilt the lens. The adapter is, in my opinion, extremely well built and has quickly become an integral component of my Sony A7r body. Since I am using almost exclusively old manual lenses (Leica R, Olympus Zuiko, Voigtländer) that are permanently adapted to a Canon EF mount (with a Leitax replacement mount), I hardly ever take the adapter off the camera. If you want to learn more about the Canon EF - Sony E mount tilt-shift adapter, head over to the excellent review at "on landscape" or post a question as a comment to this posting.
P.S. I have bought the tilt-shift adapter that is described here as a regular customer from Mirex. I am not associated with Mirex and I do not receive any form of compensation for writing this text.