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We investigate closed, symmetric $L^2(\mathbb{R}^n)$-realizations $H$ ofSchr\"odinger-type operators $(- \Delta+V)\upharpoonright_{C_0^{\infty}(\mathbb{R}^n \setminus \Sigma)}$ whosepotential coefficient $V$ has a countable number of well-separatedsingularities on compact sets $\Sigma_j$, $j \in J$, of $n$-dimensionalLebesgue 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, $\mathrm{def}(H_j)$, ofclosed, symmetric $L^2(\mathbb{R}^n)$-realizations of $(- \Delta +V_j)\upharpoonright_{C_0^{\infty}(\mathbb{R}^n \setminus \Sigma_j)}$ withpotential coefficient $V_j$ localized around the singularity $\Sigma_j$, $j \inJ$, 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, andhence both sides equal $\infty$. We first develop an abstract approach to thequestion of decoupling of deficiency indices and then apply it to the concretecase 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 ofthe 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 toSchr\"odinger-type operators in $L^2(\mathbb{R}^n)$.  Extensions to second-order (locally uniformly) elliptic differentialoperators on $\mathbb{R}^n$ with a possibly strongly singular potentialcoefficient are treated as well.

Decoupling of Deficiency Indices and Applications to Schr\"odinger-Type Operators with Possibly Strongly Singular Potentials