Stationary antichains modulo the nonstationary ideal

In ZFC, for regular uncountable $\kappa$, a stationary antichain modulo ${\mathrm{N}\mathrm{S}}_{\kappa }$ is a family $\mathcal{A}$ of stationary subsets of $\kappa$ such that $S\cap T$ is nonstationary whenever $S,T\in \mathcal{A}$ are distinct. Write $S{=}_{\mathrm{N}\mathrm{S}}T$ when $S\mathrm{△}T$ is nonstationary, where $\mathrm{△}$ here denotes symmetric difference, not diagonal intersection. This is an equivalence relation: transitivity follows from $S\mathrm{△}U\subseteq (S\mathrm{△}T)\cup (T\mathrm{△}U)$ and the ideal axioms.

An actually disjoint family of stationary sets is in particular such an antichain. Questions about bounds beyond the $\kappa$-sized partitions just constructed belong to the later large-cardinal and ideal theory; no saturation or consistency theorem is asserted here.