Fatty Acid Synthesis of Longer than 16 Carbons

I understand that the human body when performing Fatty Acid Synthesis can synthesize only until C16 (palmitate). However the ER has desaturases and elongases. I know that elongases are used to add double bonds, but do humans have desaturases to add even more Carbons to a double bond? If so, then this would mean that the human body can synthesize fats longer than C16?

Lets take a hypothetical case and say that humans have both desaturases and elongases. Would it be feasible to add double bonds to palmitate via desaturases, then add more carbons to the chain via elongases and then add more double bonds via desaturases? This way, the resulting fatty acid will have an increased length and more unsaturated character (ie more d-bonds than the prescribed 4 that humans can add at positions 4, 5, 6, and 9)?