Critical to epithelial cell viability is homeostasis of cell volume and composition during changes in transcellular transport. Two previously developed mathematical models (principal cell of the collecting duct and proximal tubule cell) are approximated by their linearizations about a reference condition. This yields matrices which estimate cell volume, cell composition, and transcellular fluxes in response to perturbations of bath conditions and membrane transporter activity. These approximations are themselves extended with the inclusion of linear dependence of membrane transport coefficients on cell variables (e.g. volume, solute concentrations, or electrical potential). This provides cell models with variable permeabilities, which may be homeostatic, and which can be examined systematically: sequentially testing each membrane permeability and its controlling cell variable. In the proximal tubule approximation, volume-mediated increase in peritubular K-Cl or Na-3HCO3 cotransport, and volume-mediated decrease in Na,K-ATPase activity are homeostatic; modulation of peritubular K permeability has little impact. In the principal cell model, volume homeostasis is afforded by volume-sensitive peritubular Na/H exchange. Predictions from the linear analysis are confirmed in the full models. This approach yields a systematic examination of homeostasis in an epithelial model, and identifies candidate control parameters.