  For a central, not necessarily reduced, hyperplane arrangement $f$ equipped
with any factorization $f = f_{1} \cdots f_{r}$ and for $f^{\prime}$ dividing
$f$, we consider a more general type of Bernstein--Sato ideal consisting of the
polynomials $B(S) \in \mathbb{C}[s_{1}, \dots, s_{r}]$ satisfying the
functional equation $B(S) f^{\prime} f_{1}^{s_{1}} \cdots f_{r}^{s_{r}} \in
\text{A}_{n}(\mathbb{C})[s_{1}, \dots, s_{r}] f_{1}^{s_{1} + 1} \cdots
f_{r}^{s_{r} + 1}.$
  Generalizing techniques due to Maisonobe, we compute the zero locus of the
standard Bernstein--Sato ideal in the sense of Budur (i.e. $f^{\prime} = 1)$
for any factorization of a free and reduced $f$ and for certain factorizations
of a non-reduced $f$. We also compute the roots of the Bernstein--Sato
polynomial for any power of a free and reduced arrangement. If $f$ is tame, we
give a combinatorial formula for the roots lying in $[-1,0).$
  For $f^{\prime} \neq 1$ and any factorization of a line arrangement, we
compute the zero locus of this ideal. For free and reduced arrangements of
larger rank, we compute the zero locus provided $\text{deg}(f^{\prime}) \leq 4$
and give good estimates otherwise. Along the way we generalize a duality
formula for $\mathscr{D}_{X,\mathfrak{x}}[S]f^{\prime}f_{1}^{s_{1}} \cdots
f_{r}^{s_{r}}$ that was first proved by Narv\'aez-Macarro for $f$ reduced,
$f^{\prime} = 1$, and $r = 1.$
  As an application, we investigate the minimum number of hyperplanes one must
add to a tame $f$ so that the resulting arrangement is free. This notion of
freeing a divisor has been explicitly studied by Mond and Schulze, albeit not
for hyperplane arrangements. We show that small roots of the Bernstein--Sato
polynomial of $f$ can force lower bounds for this number.
