  Alspach [{\sl Bull. Inst. Combin. Appl.}~{\bf 52} (2008), 7--20] defined the
maximal matching sequencibility of a graph $G$, denoted~$ms(G)$, to be the
largest integer $s$ for which there is an ordering of the edges of $G$ such
that every $s$ consecutive edges form a matching. In this paper, we consider
the natural analogue for hypergraphs of this and related results and determine
$ms(\lambda\mathcal{K}_{n_1,\ldots, n_k})$ where
$\lambda\mathcal{K}_{n_1,\ldots, n_k}$ denotes the multi-$k$-partite $k$-graph
with edge multiplicity $\lambda$ and parts of sizes $n_1,\ldots,n_k$,
respectively. It turns out that these invariants may be given surprisingly
precise and somewhat elegant descriptions, in a much more general setting.
