We consider densely defined sectorial operators $A_\pm$ that can be written
in the form $A_\pm=\pm iS+V$ with
$\mathcal{D}(A_\pm)=\mathcal{D}(S)=\mathcal{D}(V)$, where both $S$ and $V\geq
\varepsilon>0$ are assumed to be symmetric. We develop an analog to the
Birmin-Krein-Vishik-Grubb (BKVG) theory of selfadjoint extensions of a given
strictly positive symmetric operator, where we will construct all maximally
accretive extensions $A_D$ of $A_+$ with the property that
$\overline{A_+}\subset A_D\subset A_-^*$. Here, $D$ is an auxiliary operator
from $\ker(A_-^*)$ to $\ker(A_+^*)$ that parametrizes the different extensions
$A_D$. After this, we will give a criterion for when the quadratic form
$\psi\mapsto\mbox{Re}\langle\psi,A_D\psi\rangle$ is closable and show that the
selfadjoint operator $\widehat{V}$ that corresponds to the closure is an
extension of $V$. We will show how $\widehat{V}$ depends on $D$, which ---
using the classical BKVG-theory of selfadjoint extensions --- will allow us to
define a partial order on the real parts of $A_D$ depending on $D$.
Applications to second order ordinary differential operators are discussed.