In solution, the eight BF4− counterions of a positively charged D4-symmetric interpenetrated [Pd4ligand8]8+ double cage (1) are localized in distinct positions. At low temperatures, one BF4− ion is encapsulated inside the central pocket of the supramolecular structure, two BF4− ions are bound inside the equivalent outer pockets, and the remaining five BF4− ions are located outside the cage structure (expressed by the formula [3 BF4@1][BF4]5). On warming, the two BF4− ions in the outer pockets are found to exchange with the exterior ions in solution whereas the central BF4− ion stays locked inside the central cavity (here written as [BF4@1][BF4]7). The exchange kinetics were determined by exchange spectroscopy (EXSY) NMR experiments and line-shape fitting in different solvents. The tremendously high affinity of this double cage for the binding of two chloride ions inside the outer pockets allows for complete exchange of two BF4− ions by the addition of solid AgCl to give [2 Cl+BF4@1][BF4]5. The uptake of the two chloride ions is allosteric and is thus accompanied by a structural rearrangement (compression along the Pd4 axis) of the double cage structure. An analysis by using 900 MHz NOESY NMR spectroscopy shows that this compression of about 3.3 % is associated with a helical twist of 8°, which together resemble a screw motion. As a consequence of squeezing each of the outer two pockets by 53 %, the volume of the central pocket is increased by 43 %, which results in an increase of 36 % in the 19F spin-lattice relaxation time (T1) of the central BF4− ion. The packing coefficients (PC) for the ions in the outer pockets (103 % for BF4− and 96 % for Cl−) were calculated.