>> I was thinking I could do it with CSG, but then realised it's not
>> possible as the 'sphere's in the corners aren't spheres -- not even
>> scaled spheres.
>
>   The problem is not that the corners would not be spherical (I don't
> understand why they couldn't be).

Well it depends on "how" smooth you want the corners to be.  In some
situations it would be impossible to use a sphere to get a smooth join with
all three rounded edges.

> The problem is that if each corner
> has a sphere of different radius, the sides of the box become
> non-planar.

Which is why you don't use spheres...

See attachment for adding various rounds to a box, the sides stay plane, but
there are all sorts of weird transitions.  FWIW there are many different
transitions to choose from, I guess each offering a different level of
continuity.

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