Synthesis of Fatty Acids Longer than 16 Carbons
Short Answer: Yes.
Long Answer: See this article:

The diagrams presented show how fatty acids are synthesized in microorganisms and list the enzymes found in Escherichia coli. These reactions are performed by fatty acid synthase II (FASII), which in general contain multiple enzymes that act as one complex. FASII is present in prokaryotes, plants, fungi, and parasites, as well as in mitochondria.
In animals, as well as some fungi such as yeast, these same reactions occur on fatty acid synthase I (FASI), a large dimeric protein that has all of the enzymatic activities required to create a fatty acid. FASI is less efficient than FASII; however, it allows for the formation of more molecules, including &quot;medium-chain&quot; fatty acids via early chain termination.
Once a 16:0 carbon fatty acid has been formed, it can undergo a number of modifications, resulting in desaturation and/or elongation. Elongation, starting with stearate (18:0), is performed mainly in the ER by several membrane-bound enzymes. The enzymatic steps involved in the elongation process are principally the same as those carried out by FAS, but the four principal successive steps of the elongation are performed by individual proteins, which may be physically associated.


Another article from NCBI states:

Primers for several mouse, rat, and human elongases have been reported elsewhere.

...and cites here for this:

Fatty acid elongases and desaturases play an important role in hepatic and whole body lipid composition. We examined the role that key transcription factors played in the control of hepatic elongase and desaturase expression...In conclusion, these studies establish a role for PPARalpha, LXR, SREBP-1, ChREBP, and MLX in the control of hepatic fatty acid elongase and desaturase expression and lipid composition.

Indeed, humans do synthesize stearic acid (C18) in their body; mainly liver and adipose tissue. See this article:

Fatty acid biosynthesis from acetyl-CoA takes place primarily in the liver, adipose tissue, and mammary glands of higher animals. Successive reduction and dehydration reactions yield saturated fatty acids up to a 16-carbon chain length. Stearic acid is synthesized by the condensation of palmitoyl-CoA and acetyl-CoA in the mitochondria, and oleic acid is formed via a mono-oxygenase system in the endoplasmic reticulum.

Now, would it be feasible or not to synthesize unsaturated fatty acids is a matter of debate. Maybe this could be helpful in this matter.