I suspect the way to achieve this would be the same way GenX allows you to create different sub-groups, which I strongly suspect (but don’t know for certain) is common across all the Genesis morphs. (I haven’t looked at Gen 4 or other figures to check whether it is common to them too, but don’t see any reason for DAZ developing two separate sets of functionality for displaying morphs).
If you go down into /data/DAZ 3D/Genesis/Base/Morphs/DAZ 3D/Base you will find the .dsf files for all of the basic Genesis morphs. If you open one up in a text editor, and search for ‘group’, then the line of text it finds (near the bottom of the first screen of text in all the examples I’ve looked at) will say something like:
“group” : “/Pose Controls/Head/Eyes”,
Which if you compare with the parameters pane corresponds exactly with the hierarchical breakdown presented to you there. So the way to achieve what you want is likely to be to edit the ‘group’ entries in the individual .dsf files. Normal caveats apply - i.e. I haven’t actually done this myself yet, and either take back-ups or be prepared to reinstall any morph package you change in case it causes unforeseen problems.
Looking in the GenX folder, where I have edited Group entries, there is also an entry immediately above the ‘Group’ line:
“region” : “Actor”,
And the GenX morphs appear within the Actor category on the Parameter pane, so there are potentially two relevant entries here. I’ve got my GenX V3 category subdivided into Head and Body, and ISTR I actually did edit the group line in some of the .dsfs to create that sub-division - and a quick experiment confirms that you can definitely add a new subgroup using this method.