The symmetric-group multifold-factorization conjecture

Let $S_n$ denote the symmetric group of degree $n$, and let “multifold-factorizable” have the meaning defined in the paper. Symmetric-group multifold-factorization conjecture. The symmetric group $S_n$ is multifold-factorizable for all $n\geq 2$. The paper suggests this as a potentially easier statement to prove, but the supplied text gives no proof or disproof.