Mmmmm, I spoke too soon.
Placing one uiGroup on top of another one automatically makes the one on top a member of the lower group. So that means that setting the lower uiGroup invisible automatically makes all the other uiGroups on top of it invisible as well. If you set both uiGroups visible then you end up with a jumble of modulators from both groups all visible at the same time, which is not what I was after at all!
Removing the ‘Component Generic – Group’ setting or unticking the ‘Is component a member of a group’ doesn’t seem to make any difference. If you have one uiGroup on top of another one then it belongs to the lower group and that’s that!
I’m going to take a break and see if any divine inspiration strikes me when I’m doing something else 🙂