  If a graph is $n$-colourable, then it obviously is $n'$-colourable for any
$n'\ge n$. But the situation is not so clear when we consider multi-colourings
of graphs. A graph is $(n,k)$-colourable if we can assign each vertex a
$k$-subset of $\{1,2,\ldots,n\}$ so that adjacent vertices receive disjoint
subsets. In this note we consider the following problem: if a graph is
$(n,k)$-colourable, then for what pairs $(n', k')$ is it also
$(n',k')$-colourable? This question can be translated into a question regarding
multi-colourings of Kneser graphs, for which Stahl formulated a conjecture in
1976. We present new results, strengthen existing results, and in particular
present much simpler proofs of several known cases of the conjecture.
