What might be an advantage of having more than one codon for the same amino acid?

The extra codons mean the code is more resilient - small errors can still result in the same protein being produced. The other advantage is that in some cases, a single strand of genetic material might code for more than one protein or enzyme, depending on how it is read. This means that one method of reading will produce the same output, but the second or third method of reading (starting from a different place on the strand) can produce other, entirely different materials. This concept is like a palimpsest.