You could do as a few other people have suggested, and make an intermediate positive (a.k.a. an interpositive), from which you will make the final negative. This is the method which I used for years when I used to have to make a quantity of B&W prints from a colour negative. This will also work if your original is a B&W negative.
The first step was a flat, dark interpositive on a panchromatic film. I originally used Super-XX. When it was no longer available, I used T-Max 100.
The next step was an internegative, on Kodak Professional Copy Film, also no longer available. The reason for this film was that contrast was controlled by both development and exposure, it having a compound characteristic curve. You could try a normal panchromatic film, but you may have to develop it it a higher than normal contrast developer, like D-19. You will find that extending the times in a developer like D-76 or HC-110 won't give you the contrast you will need to get a decent negative.
Contact is the way to go, if possible. If you are making this duplicate negative because you want a large negative for contact printing or because you need a large negative for very large enlargements, then you should make the interpositive by contact, and the internegative by projection. The reason for this is that dust will be a major problem, and dust on the original negative will be white on the interpositive, and will ultimately be white on the final print, which is relatively easy to retouch. If you get dust on the interpositive, it will be black on the final print, which can be very difficult to retouch. If you make the internegative via projection, it is somewhat easier to keep clean than a contact internegative.
E-mail me if you want further details.