I know that this isn't a popular answer but I'll repeat myself...with the caveat that the only 380 ACP die set I have is from Hornady. I also have 9mm die sets from Lyman, Lee, and Hornady.
Tonight I resized 100 cases with my Hornady 9mm sizing die. These were primed cases, so I backed out the decapping pin first.
Next, I took out my 380 ACP die set (Hornady Item #546518) and removed the Expander die Hornady Item #044517), loosened the lock ring and backed it out of the LNL Bushing. I put the Hornady 9mm shellholder in place on the press (Hornady Item # 390548, or #8), then adjusted the 380 ACP expander die to flare the 9mm case enough to hold the 9mm FMJ bullet that I keep in my drawer for this purpose. After setting the amount of expansion that I wanted (very little...enough to push the bullet in place, not enough to just set the bullet on top...spilled too many powdered cases doing that). I proceeded to expand the remaining 99 PMC brass cases.
My next step was to change the shell holder back to the 380 ACP, in this case I have a Redding #10 shellholder. I don't trim 380ACP cases, so I never saw the need to buy a Hornady 380 ACP shellholder (Hornady Item #390556, or #16). I then readjusted the expander die to 380ACP, as it normally sits in the case, using the same .355 FMJ profile that I keep in my drawer.
The next step is to take the Hornady 380 ACP Bullet Seating Die (Hornady Item #044144). Again, it's normally set for 380 ACP, so I need to loosen the lock ring and back out both the die body and the seating stem. Using the 9mm shellholder, I place the expanded 9mm case into position and adjust the die body down to kiss the mouth of the case, then back off 1-2 turns. Then I tighten the lock ring. Next I place the 9mm projectile on top of the case (empty as I'm just working through the motions to illustrate this point. That point being: .355 or .356 is .355 or .356, whether it sits atop a 380ACP case or a 9mm (9x19) case).
I adjust the seating stem until it contacts the bullet, then begin dialing in the seating depth that I want. In my zeal I actually went past 1.150" that I was aiming for and seated this first dummy to 1.120" No biggie as the point is proved that a 380 ACP die will accommodate a 9mm case and seat a bullet to desired depths from 1.169" to wherever you want it to be.
I took the additional step of backing everything out, resetting the seating die for a 380ACP case, and seated a 100gr HBRN (familiar Berry's projectile) to 0.965", yes, once again in my zeal I went past the 0.980" I was targeting. This was corrected for the next round.
The last step is crimping. Here the story is a little different. The Lee 380ACP FCD cannot be used reliably to remove the flare from a 9mm case. However, the Hornady 9mm Taper Crimp Die (Hornady Item #044170) will easy put a proper taper crimp on a 9mm cartridge as well as on a 380ACP cartridge.
More specifically, if one desired to assemble a single die set to handle both 380ACP and 9mm, you could purchase a 380 ACP 3 die set or a 9mm Luger 3 die set. You will then purchase shell holders for 380 ACP and 9mm, as well as either Taper Crimp Die and only the Sizing Die for the other caliber.
Finally, if you go to this url
https://www.hornady.com/reloading/reloading-essentials#!/d/1732, you can search for 380ACP and 9mm Luger, and you'll see that most of the part numbers are identical.
