  A famous conjecture of Ryser states that every $r$-partite hypergraph has
vertex cover number at most $r - 1$ times the matching number. In recent years,
hypergraphs meeting this conjectured bound, known as $r$-Ryser hypergraphs,
have been studied extensively. It was recently proved by Haxell, Narins and
Szab\'{o} that all $3$-Ryser hypergraphs with matching number $\nu > 1$ are
essentially obtained by taking $\nu$ disjoint copies of intersecting $3$-Ryser
hypergraphs. Abu-Khazneh showed that such a characterisation is false for $r =
4$ by giving a computer generated example of a $4$-Ryser hypergraph with $\nu =
2$ whose vertex set cannot be partitioned into two sets such that we have an
intersecting $4$-Ryser hypergraph on each of these parts. Here we construct new
infinite families of $r$-Ryser hypergraphs, for any given matching number $\nu
> 1$, that do not contain two vertex disjoint intersecting $r$-Ryser
subhypergraphs.
