  Let $P \subseteq \mathbb{R}^2$ be a set of points and $T$ be a spanning tree
of $P$. The \emph{stabbing number} of $T$ is the maximum number of
intersections any line in the plane determines with the edges of $T$. The
\emph{tree stabbing number} of $P$ is the minimum stabbing number of any
spanning tree of $P$. We prove that the tree stabbing number is not a monotone
parameter, i.e., there exist point sets $P \subsetneq P'$ such that
\treestab{$P$} $>$ \treestab{$P'$}, answering a question by Eppstein \cite[Open
Problem~17.5]{eppstein_2018}.
