  Given $k$ pairs of vertices $(s_i,t_i)\;(1\le i\le k)$ of a digraph $G$, how
can we test whether there exist vertex-disjoint directed paths from $s_i$ to
$t_i$ for $1\le i\le k$? This is NP-complete in general digraphs, even for $k =
2$, but in an earlier paper we proved that for all fixed $k$, there is a
polynomial-time algorithm to solve the problem if $G$ is a tournament (or more
generally, a semicomplete digraph). Here we prove that for all fixed $k$ there
is a polynomial-time algorithm to solve the problem when $V(G)$ is partitioned
into a bounded number of sets each inducing a semicomplete digraph (and we are
given the partition).
