  We investigate closed, symmetric $L^2(\mathbb{R}^n)$-realizations $H$ of
Schr\"odinger-type operators $(- \Delta
+V)\upharpoonright_{C_0^{\infty}(\mathbb{R}^n \setminus \Sigma)}$ whose
potential coefficient $V$ has a countable number of well-separated
singularities on compact sets $\Sigma_j$, $j \in J$, of $n$-dimensional
Lebesgue measure zero, with $J \subseteq \mathbb{N}$ an index set and $\Sigma =
\bigcup_{j \in J} \Sigma_j$. We show that the defect, $\mathrm{def}(H)$, of $H$
can be computed in terms of the individual defects, $\mathrm{def}(H_j)$, of
closed, symmetric $L^2(\mathbb{R}^n)$-realizations of $(- \Delta +
V_j)\upharpoonright_{C_0^{\infty}(\mathbb{R}^n \setminus \Sigma_j)}$ with
potential coefficient $V_j$ localized around the singularity $\Sigma_j$, $j \in
J$, where $V = \sum_{j \in J} V_j$. In particular, we prove \[ \mathrm{def}(H)
= \sum_{j \in J} \mathrm{def}(H_j), \] including the possibility that one, and
hence both sides equal $\infty$. We first develop an abstract approach to the
question of decoupling of deficiency indices and then apply it to the concrete
case of Schr\"odinger-type operators in $L^2(\mathbb{R}^n)$.
  Moreover, we also show how operator (and form) bounds for $V$ relative to
$H_0= - \Delta\upharpoonright_{H^2(\mathbb{R}^n)}$ can be estimated in terms of
the operator (and form) bounds of $V_j$, $j \in J$, relative to $H_0$. Again,
we first prove an abstract result and then show its applicability to
Schr\"odinger-type operators in $L^2(\mathbb{R}^n)$.
  Extensions to second-order (locally uniformly) elliptic differential
operators on $\mathbb{R}^n$ with a possibly strongly singular potential
coefficient are treated as well.
