Arrows in the category $\bf Rel$ are binary (2-valued) relations between set objects.
Do ternary, 4-term, $n$-term and variadic (2-valued) relations form categories? (Or perhaps one category?).
$n$-ary relations are mentioned in nlab, but no explicit category seems defined. Neither does the concept seem to be discussed in Freyd & Scedrov's Categories, Allegories. Did I miss it?
By analogy with graphs and hypergraphs, where the former are defined by edges between pairs of vertices, whereas the latter are defined by arbitrary subsets of vertices, it's not clear offhand how would arrows be defined even for a ternary relation $R \subset X \times Y \times Z$?