Let $\mathcal A$ be a factor von neumann algebra and $\Phi$ preserve $n$-tuple new product derivations on $\mathcal A$, that is, for every $A_1,A_2,\dots,A_n\in\mathcal A$, \begin{align*} \Phi(A_1\diamond A_2\diamond\dots\diamond A_n)=\Phi(A_1)\diamond A_2\diamond\dots\diamond A_n+A_1\diamond\Phi(A_2)\diamond\dots\diamond A_n +\dots+A_1\diamond A_2\diamond\dots\diamond\Phi(A_n) \end{align*} where $A_i\diamond A_j=A_i^*A_j-A_j^*A_i$ for $i,j\in\mathbb N$, then $\Phi$ is additive $\ast$-derivation, on the condition that $\Phi\big(\alpha\frac I2\big)$ is self-adjoint operator for $\alpha\in\{1,i\}$.