Terpy embraces (TE) are intermolecular motifs involving metal complexes of the type [M(terpy)2]2+ (terpy = 2,2′:6′,2″-terpyridine), based on concerted offset-face-to-face (OFF) and edge-to-face (EF) interactions between pyridyl rings. These embraces are well known to occur as extended two-dimensional grid motifs in crystals (called two-dimensional terpy embraces, 2D-TE). We have previously enunciated the layer-stacking principles for 2D-TE when the complexes are associated with monoanions which occupy cavities within grooves on the surfaces of the layers. We introduce here two new features of terpy embraces in crystals: (a) the use of tetrahedral dianions to control the stacking of layers and (b) an alternative layer motif, namely the two-dimensional inverted chain terpy embrace (2D-IC-TE). The standard 2D-TE is constructed with only translation of complexes, while the 2D-IC-TE also possesses inversion centres between complexes in the layer. The density of local OFF and EF interactions in the new 2D-IC-TE is the same as that in the standard 2D-TE, but the surfaces of the layers possess a halved number of enlarged troughs. In crystal [Ni(terpy)2](SO4)(nPrOH)4, 1, the orthogonal SO2 fins of dianionic sulfate engage the shallow grooves of the standard 2D-TE grids of [Ni(terpy)2]2+ complexes, causing them to stack in a fashion not previously observed. With a larger tetrahedral dianion, HgI42−, in crystal [Ni(terpy)2](HgI4), 2, the alternative 2D-IC-TE grids of [Ni(terpy)2]2+ complexes occur, with the anions occupying the troughs. Variation of the ligand to terpyOH (4-hydroxy-2,2′:6′,2″-terpyridine), with sulfate, yields crystals [Ni(terpyOH)2](SO4)(MeOH)(EtOH)(H2O)0.5, 3, which also contain 2D-IC-TE grids. Half of the sulfate together with methanol and ethanol occupy the troughs, and a hydrogen bonding network links terpyOH, MeOH, EtOH, SO42− and water. Two related crystal structures, [CoIII(terpyOH)(terpyO)](SO4)(EtOH)3(H2O)4, 4, and [CoIII(terpyOH)(terpyO)](BF4)2(H2O)4.5, 5, are also described. They are dominated by hydrogen bonding networks, and contain no terpy embraces. The one known related structure with no anions, [Ru(terpy)2]0 [CSD LOCRIE], is also analysed in detail for the first time. It contains modified 2D-IC-TE layers, interleaved with twinned pairs of one-dimensional TE chains. There are multiple OFF and EF interactions at the interfaces of these two motifs, but no new concerted embrace motifs. Analysis of this structure in the context of conventional [M(terpy)2]2+ complexes provides some guidance for the engineering of two-dimensional grids.