A practice that some soapmakers do is to add the oil of superfat in the trace thinking mistakenly that oil is what will remain unaffected unsaponified in the finished soap, i.e. without reacting with lye. This is one of the myths that populate the world of handmade soapmaking, is so rooted that even in books you can find this practice.

Nothing like a theory and a scientific trial to overturn myths.  Was what made Kevin Dunn in his work: Superfatting and the Lye Discount. This chemistry teacher is the only chemical that has been dedicated to making a scientific and systematic way has it, contributed objectively to explain the phenomena of handmade soap manufacture.

Here is the article of Prof. K. Dunn:

Superfatting and the lye discount.pdf