An important feature of MaxIm DL is that it stores images internally in 32-bit floating-point format. Although this increases memory consumption compared to standard desktop image editing programs, it gives much greater flexibility and helps preserve data precision.
If you were to sum or average together 256 individual 16-bit images, the actual bit depth of the result could be as high as 24 bits. In reality, you probably have only 12 to 14 bits of usable data in each image; nevertheless the final result would still have 20 to 22 bits. Obviously if you store this result in a 16-bit or 8-bit file format, you will need to rescale the image and clip and/or truncate part of the useful data. If you scale the image so that you maintain faint image detail and good background statistics, you will end up clipping off the brighter objects. Therefore when working with images like this, it is best to save them in FITS format with IEEE Float pixel format.
Most desktop image editing programs only work at 8 bits, or 16 bits at most. Even if you plan to export data to a desktop editing program for final tweaks, it makes sense to do as much processing as possible at high bit depth first. When that is completed, you should save the result to a high bit depth format, and then export the data to a format compatible with your editing program. This way if you find you need to make additional adjustments you can easily go back without having to start over.