The new compartmental proligand 4-bromo-3,5-bis{6-(2,2'-bipyridyl)}pyrazole (HLBr) was synthesized and shown to form robust [2 X 2] grid complexes [(Fe4L4Br)-L-II]X-4 with various counteranions (X- = PF6-, ClO4-, BF4--, Br--). The grid [(Fe4L4Br)-L-II](4+) is stable in solution and features two high-spin (HS) and two low-spin (LS) ferrous ions in frozen MeCN, and its redox properties have been studied. Six all-ferrous compounds [Fe4L4Br]X-4 with different counteranions and different lattice solvent (la-f) were structurally characterized by X-ray diffraction, and their magnetic properties were investigated by Mossbauer spectroscopy and SQUID magnetometry. Variations in spin-state for the crystalline material range from the [4HS] via the [3HS-1LS] to the [2HS-2LS] forms, with some grids showing thermal spin crossover (SCO). The series of [(Fe4L4Br)-L-II](4+) compounds allowed us to establish experimentally well-grounded correlations between structural distortion of the {FeN6} coordination polyhedra, quantified by using continuous shape measures, and the grid's spin-state pattern. These correlations evidenced pronounced cooperativity for the multistep SCO transitions within the grid, imparted by the strain effects of the rigid bridging ligands, and a high stability of the dimixed-spin configuration trans-[2HS-2LS] that has identical sites at opposite corners of the grid. The results are in good agreement with recent quantum chemical calculations for such molecular [2 X 2] grids featuring strongly elastically coupled vertices.