Cells lacking a stiff cell wall, e.g., mammalian cells, must actively regulate their volume to maintain proper cell function. On the time scale that protein production is negligible, water flow in and out of the cell determines the cell volume variation. Water flux follows hydraulic and osmotic gradients; the latter is generated by various ion channels, transporters, and pumps in the cell membrane. Compared to the widely studied roles of sodium, potassium, and chloride in cell volume regulation, the effects of proton and bicarbonate are less understood. In this work, we use mathematical models to analyze how proton and bicarbonate, combined with sodium, potassium, chloride, and buffer species, regulate cell volume upon inhibition of ion channels, transporters, and pumps. The model includes several common, widely expressed ion transporters and focuses on obtaining generic outcomes. Results show that the intracellular osmolarity remains almost constant before and after cell volume change. The steady-state cell volume does not depend on water permeability. In addition, to ensure the stability of cell volume and ion concentrations, cells need to develop redundant mechanisms to maintain homeostasis, i.e., multiple ion channels or transporters are involved in the flux of the same ion species. These results provide insights for molecular mechanisms of cell volume regulation with additional implications for water-driven cell migration.