Absent any compression (these cameras are all 14-bit uncompressed, and compressed options that some have start with a 14-bit signal), it takes 1 bit of data to represent 1 stop of dynamic range (per pixel, and per color channel). The only theoretical way to get more than 14 stops of signal is to use a 16-bit (or higher) analog to digital converter, which is much more expensive, slower and unnecessary for all but a few medium format sensors.
According to a prior discussion on Luminous, the only current sensor to have a 16-bit data path is the Sony 100 MP "645 full-frame" sensor in a few Phase One backs. Previous medium-format sensors that claimed "16-bit" files were apparently just taking a 14-bit output and adding a couple of zeros on the bottom (you could take an iPhone image with about 7 bits of real data, add 9 zeros and claim it as 16-bit) Since that discussion was last year, the very latest 150 MP sensor in the high-end Phase backs was not around yet, but I would guess it's also 16-bit. Another candidate that we should see soon is the new 100 MP 33x44 mm sensor that will show up in the successors to the Hasselblad H1D and Fuji GFX - that is unclear, because it is much more of a mass-market sensor - sort of. The medium format mirrorless cameras probably sell in the low tens of thousands per year, while the top Phase backs sell in the hundreds or maybe low thousands - for comparison, Nikon can make 240,000 Z7's per year, and I suspect A7rIII's, EOS-R's, etc. are in the same range, as are top-end DSLRs - say a million total cameras at or over 36 MP annually. Also, no medium-format camera shoots much over 1 FPS - there's time to move the extra data around.
The current Sony 24x36mm sensor seems to be right on the verge of producing more than 14 bits of real, usable data. Measurements of photographic dynamic range (which can underestimate - there are decisions in determining where the signal fades into noise, and Photons to Photos is conservative) show over 12 stops of highly usable dynamic range, and you can stretch another stop in the shadows. A 16-bit converter won't help this generation, but it might be necessary for the next generation.
One possible approach is that the Nikon D3x, the first camera outside of medium format to actually need 14-bit processing (because it could record more than 12 bits of real data) didn't have a true 14-bit converter, but it had some way of reading the analog values several times on the same exposure and running it through the analog to digital converter at different gains. It slowed the camera down by a factor of four, but it got 14-bit data out of a 12-bit converter. I wouldn't be at all surprised to see someone do that with an upcoming sensor. The D3x in slow mode was something like a 1.3 fps camera, but it sure produced a nice file... By the time the D800 came along, Nikon had a true 14-bit converter that ran at a more standard frame rate.
Dan