Two-dimensional slices of non-pseudoconvex open sets

Let $D$ be a non-pseudoconvex open set in ${\text{C}}^3$ and $S$ be the union of all two-dimensional planes with non-empty and non-pseudoconvex intersection with $D\mathrm{.}$ Sufficient conditions are given for ${\text{C}}^3\setminus S$ to belong to a complex line. Moreover, in the ${\mathcal{C}}^2$-smooth case, it is shown that $S={\text{C}}^n$.