We investigate how the elastic properties of a two-solvent lyotropic lamellar phase are modified by the addition of a nonadsorbing water-soluble homopolymer (polyvynilpyrolidone). The initial two-solvent lyotropic lamellar phase consists of a regular stack of surfactant monolayers made from a mixture of nonionic surfactants (TX100/TX35) and a cationic surfactant (cetylpyridinium chloride) which separate successive layers of oil (decane) or water. By modifying the relative proportions of the various components of the lamellar phase or the temperature, we are able to control the magnitudes of the different contributions to physical interactions between the bilayers. From small-angle X-ray measurements on this system, we have identified four different critical L-alpha/L-alpha phase separations. At such critical points the corresponding smectic susceptibility (B) over bar(-1) diverges. In an attempt to better understand these experimental results we present a general calculation of the smectic compression modulus (B) over bar of a four-component lyotropic lamellar phase. This model is applied to our specific system. This allows us to understand the occurrence of three of the observed critical points of our system.