  Let $v(n)$ be the largest principal specialization of Schubert polynomials
for layered permutations $v(n) := \max_{w \in \mathcal{L}_n}
\mathfrak{S}_w(1,\ldots,1)$. Morales, Pak and Panova proved that there is a
limit \[\lim_{n \to \infty} \frac{\log v(n)}{n^2},\] and gave a precise
description of layered permutations reaching the maximum. In this paper, we
extend Morales Pak and Panova's results to generalized principal specialization
$\mathfrak{S}_w(1,q,q^2,\ldots)$ for multi-layered permutations when $q$ equals
a root of unity.
