Both of these suggestions are clever, and I probably wouldn't have thought of the first one and clearly didn't think of the second!
As far as my original question is concerned, I appreciate the quick response from GarryP. I'm not surprise that this isn't possible, since it seems to me that layers are a fairly fundamental part of Designer. (And Gary, thanks for pointing out the apparent error. The top half of the collar doesn't need to be in two parts: I just haven't got round to combining both yet).
I wonder if my problem could be solved if objects (possibly layers) were associated with a "set". I could then leave the grouping as is, but associate each component with the set "collar". That would give me the organisation I'm looking for whilst still leaving the objects themselves in their current layers. I appreciate I need the layers to get the effect, but I only want to connect the objects to keep them clearly associated in the layers list. This is a feature request, I suspect, and so not something that ought to be raised here, but maybe someone sees another solution with this prompting?
Again, thanks for the very helpful responses and suggestions. Much appreciated.