Working in a suitable extension of $\sf ZF-Reg.$, can we have a transitive model $M$ of $\sf ZF-Reg.$ such that for every set in $M$ there is a partition on it in $M$ all compartments of which are non-singleton finite sets. And such that any subset $X$ of $M$ that is a family of pairwise disjoint larger than singleton finite sets then $X \in M$.