Let $k\in\mathbb N$. Given a finite graph with two subsets of vertices $X$ and $Y$, Menger's Theorem gives a criterion for when there are $k$ pairwise disjoint paths starting in $X$ and ending in $Y$.

Now let $X_1$, $Y_1$, $\dots$,$X_k$, $Y_k$ be subsets of vertices. Is there a "similar" condition for when there are $k$ pairwise disjoint paths, one path starting in $X_1$ and ending in $Y_1$, a second path starting in $X_2$ and ending in $Y_2$, $\dots$, and a $k^{\text {th}}$ path starting in $X_k$ and ending in $Y_k$?