The possibility of increasing the degree of multiplexing of twisted nematic cells has been investigated by taking the following factors into consideration: unequal elastic constants and arbitrary dielectric anisotropy for the liquid crystal medium, and a general anisotropic interfacial potential. It can be shown that the achievable degree of multiplexing of twisted nematic cells under the nonrigid boundary condition can be improved by a factor of 10 to 50 over the case of the rigid boundary condition, in contradiction to a factor of two predicted by Nehring, Kmetz, and Scheffer [J. Appl. Phys.47, 850 (1976)]. The effect on the degree of multiplexing by different forms of the anisotropic interfacial potential is also discussed.