Hi MJKoski, thank you for your input in the other threads. I wanted to experience this issue first hand so I took the plunge and spent a few thousand shutter actuations trying to get some useful data. I don't own a K-1, only a K-70, so the differences may be due to the different camera models.
I lit a white-ish wall with an LED light to create a surface with varying brightness and shot it using "Average" multiple exposure mode. I did a single shot, 2 exposures, 4, 8, 16, 32, 128, and 500 exposures. I wanted to see if the magenta casting is somewhat gradual or whether it only happens after a hitting a certain threshold. The results can be seen below.
The amount of magenta I see in the pictures slightly vary from picture to picture, but I did not see a consistent pattern of increasing magenta as the number of shots increases, nor a significant jump between the single exposure and the 500. I exaggerated the effect below, but my conclusion did not change.
A mistake, however, was made prior to this experiment. I first tried a single shot and compared it with a 128 shot multi-exposure, and there it was, the magenta casting. However, then, I realized that I had just shot the 128 shot multi-exposure using the "comparative brightness" mode. Here there is definitely an increase in magenta.
So, I must ask you, is there any chance that you were using the "comparative brightness" mode instead of averaging when you got the heavily magenta-casted shots? I only ask because I myself actually made that mistake when I conducted the experiment, as described above. In addition, the linear streaks and colorfully saturated highlights (clouds, reflections) in your sample shot is not that dissimilar from sample shots of Olympus's Live-Composite mode (e.g.,
https://www.creativeislandphoto.com/uploads/1/0/5/1/10515211/clouds-pb-small_orig.jpg), which is a similar type of exposure to comparative brightness multi-exposure. One more thing that gave me the idea of this possibility is that the picture of chunks of snow moving around in a body of water in your thread (
Long exposure vs Average Interval Composite - PentaxForums.com) is described as an example of a 512 frame Averaging shot, but it seems to be a "comparative brightness" shot -- the chunks of snow at the time of each exposure should not be so opaque if they were averaged with 511 other exposures in which the chunk is no longer there.
For easier reference, I will embed the single shot Average, 500-exposure Average, single shot Bright, 128-exposure Bright samples below, all developed to exaggerate the effect and cropped. The last two images are further cropped in "single shot Average" vs "500-exposure Average", to demonstrate how Averaging does seem to give you advantages in shadow noise, even at extreme settings such as 500 shots. (In, K-70, at least).
single shot Average
500-exposure Average
single shot Bright
128-exposure Bright
single shot (above) vs 500 shot (below) averaging. Noise is smoothed out in the shot below.