  We here present a method of performing integrals of products of spherical
Bessel functions (SBFs) weighted by a power-law. Our method, which begins with
double-SBF integrals, exploits a differential operator $\hat{D}$ defined via
Bessel's differential equation. Application of this operator raises the
power-law in steps of two. We also here display a suitable base integral
expression to which this operator can be applied for both even and odd cases.
We test our method by showing that it reproduces previously-known solutions.
Importantly, it also goes beyond them, offering solutions in terms of singular
distributions, Heaviside functions, and Gauss's hypergeometric,$\;_2{\rm F}_1$
for $all$ double-SBF integrals with positive semi-definite integer power-law
weight. We then show how our method for double-SBF integrals enables evaluating
$arbitrary$ triple-SBF overlap integrals, going beyond the cases currently in
the literature. This in turn enables reduction of arbitrary quadruple,
quintuple, and sextuple-SBF integrals and beyond into tractable forms.
