I took a look at my .380 and 9mm die sets comparred to one another and here is my opinion. (Just an opinion, since I have not tried to load .380 with a 9mm die set.
I think that there would be no problem using a 9mm seating die and 9mm taper crimp die to load .380 unless you just can't adjust the die down far enough to do its intended job.
I think you may have a problem with the expander. The working part of the 9mm expander is much longer than the working part of a .380 expander. I think you might end up expanding the full length of the .380 case before you could get a flare. You might even bottom out the expander in the .380 case.
Although I haven't tried it, I don't think a 9mm sizing die will work for .380. 9mm is a tapered case, and although the dimensions of the bullet are the same, the dimensions of the case, (just above the rim ) are very different (.391 Vs .374). The 9mm sizing die has a long tapered carbide sizing ring, the .380 sizer die does not.
tabranch I'd still like to see those pictures of the Super Star parts. You know what they say, a picture is worth a thousand words. I'm having a hard time visualising it from your description.