he collection of all finite lattices with the same poset of meet-irreducible elements is a lattice, as proved in [5]. In the present paper, it is proved that every finite Boolean lattice is isomorphic to such collection-lattice of a particular poset. It is also proved that no chain could be represented by a collection-lattice, unless it has at most two elements. However, some direct products of a chain and a lattice (or lattices) can be represented by a collection-lattice. Such a representation is proved for the direct product of a three-element chain and a finite Boolean lattice.