special relativity - Which causal structures are absent from any "nice" patch of Minkowski space?

Which "causal separation structures" (or "interval structures") can not be found among the events in "any nice patch ($P$) of Minkowski space"?,

where "causal separation structure" ($s$) should be understood as a function from $n (n - 1) / 2$ distinct pairs (formed from $n$ elements/events of some set $E$) to the set of three possible assignments of "causal separation" (namely either "timelike", or "lightlike", or else "spacelike").

Of particular interest: what's the smallest applicable number $n$? -- for which a corresponding "causal separation structure" can be expressed which can not be found among the events in patch $P$; i.e. such that $E \, {\nsubseteq} P$.

Finally: please indicate under which conditions (on which sort of patches, necessarily different from "any nice patch of Minkowski space") the proposed structure could be found instead; or otherwise, whether it is "impossible" in general.