Here we report a ferroelectric capacitor structure obtained by alternating ferroelectric and insulator thin-film layers which allows an increase of up to 2n polarization states, with n the number of ferroelectric layers. Four and up to eight distinct, stable and independently addressed polarization states are experimentally demonstrated in this work. The experimental findings are supported by a theoretical model based on the Landau-Ginzburg-Devonshire theory. The key parameter is the change in the strain conditions of ferroelectric layers induced by the insulating separator. Notably, the 2n increase in the storage capacity can be achieved without major changes in the present technology used for FeRAM devices. The test structures demonstrate very good memory characteristics such as retention and fatigue, opening the way towards the design of high density ferroelectric memories.