If that is so, I don't see why a camera couldn't record two or more ISO's at the same time and record them as different images.
Why would one want to? The raw voltages off the sensor in each case would be the same. The only difference would be the amount of amplification applied to the signal when it is digitized. Multiplying/dividing the digitized values are what we already do when post-processing raw files. In a very real sense, buy saving the raw data and processing the image with varying settings we can already do what you suggest - just not in the camera at the time the photo is exposed. Of course the more the signal is amplified when converted from analog to digital, the lower the dynamic range will be.
Having the same information recorded at two different amplification levels would not increase the dynamic range of the sensor - that is determined by the distance between the noise floor and full well capacity. But multiplying it by a greater factor can reduce the dynamic range by reducing the maximum amount of light recorded before the value for full saturation of a pixel is reached.
It's not like you could shift the shutter time or aperture value based on the varying amplification. Those would be locked in for each single exposure.
I'm asking because if this is possible, it would make ISO variable HDR photos a lot easier with no ghosting and open up possibilities in many cases where it is not used right now (fast moving objects).
You would still be limited by the sensor's physical characteristics. The difference between the minimum signal that can be distinguished from noise and the maximum signal that can be distinguished from an even higher signal is what determines the sensor's dynamic range. Assuming one is recording the raw data then it is all available to work with when editing the image.
If one is only wishing to save as a jpeg, there are already cameras that can make multiple jpegs from the raw sensor data of a single exposure and alter the the in-camera processing to produce multiple jpegs. This is usually done in terms of white balance bracketing, but it can also be done with regard to amplification/image brightness in a few cameras. I suppose it would be trivial to also do it while varying contrast as well.