On the K-3iii firmware update page there's a link to
Function Expand Firmware | PENTAX K-3 Mark III | RICOH IMAGING showing the effect of the KATEN Custom Image setting, which is only available with two specific lenses.
However, examination of the little hexagonal diagram shows a remarkable similarity to that in the 'Portrait' Custom Image setting within the camera.
There are also a set of contrast adjustments.
Is it possible someone with one of the "required" lenses could make a quick comparison between the KATEN setting (assuming they've updated their firmware to the latest level) and the Portrait setting, with the published contrast adjustments applied.
I've checked my other bodies and both the K-70 and the KP have a similar default Portrait configurations, so the contrast adjustments could be applied quite easily for a "pseudo-KATEN", if it was worth the effort.
Unfortunately my K-01, K-5 and the DCU have a different default Portrait configuration, so while DCU might be tweaked to provide a similar output, it wouldn't be possible with these two bodies.
I don't have any of the other interim bodies to check.