If I make a derivative work based on a public domain work, can I prevent other people from making additional derivative works of it?

No. Any number of people can make derivative works based on the same public domain work. If each derivative work is original , creative, authored by a human, and fixed in a tangible medium, then each creator of a derivative work can claim and register a copyright in the work he or she created. The derivative works must be original, though. If one derivative work based on a public domain work is a copy of another one, then the second derivative work does not satisfy the originality requirement for copyright protection, and only the first derivative work would receive copyright protection.