To make new proteins, you have to create new ribosomes, as it's they who interpret the RNA codons to stitch amino acids together. Bootstrapping a new ribosome is several magnitudes harder than constructing a synthetic DNA/RNA.

Actually, you don't even need new DNA letter to do that. DNA codons can encode 64 different amino acids (63, as one codon must encode the end of sequence), but only 20 amino acids are actually used.

Adding another amino acid is theoretically possible, but this would require rewriting the whole DNA to reencode, say leucine from CTG to another codon to assign CTG to some other acid.