  We give an approximate Menger-type theorem for when a graph $G$ contains two
$X-Y$ paths $P_1$ and $P_2$ such that $P_1 \cup P_2$ is an induced subgraph of
$G$. More generally, we prove that there exists a function $f(d) \in O(d)$,
such that for every graph $G$ and $X,Y \subseteq V(G)$, either there exist two
$X-Y$ paths $P_1$ and $P_2$ such that the distance between $P_1$ and $P_2$ is
at least $d$, or there exists $v \in V(G)$ such that the ball of radius $f(d)$
centered at $v$ intersects every $X-Y$ path.
