Given the functional dependencies of a relation is there more then one way to normalize it?
Normalization to Boyce-Codd Normal Form, 5NF or 6NF (and therefore to any "lesser" NFs) certainly can be automated. Google for Bernstein's alogrithm for a simple example of how.

There is frequently more than one way in which a set of dependencies can be normalized to any given Normal Form. Again, there are formal methods that can help you choose. Typically we want a database that is not just normalized but also dependency-preserving.