Many cell behaviors involve cell-shape transformations that impose considerable changes in the cell's surface area, requiring a constant adaptation of the cell's plasma membrane area to prevent cell lysis. Here, we theoretically describe the interplay between the plasma membrane dynamics and a physically connected cell cortex or wall, accounting for spatial variations in membrane recycling and tension. In-plane membrane net flows result naturally from these dynamics and, in the presence of an expanding cell cortex or wall, regions of converging or diverging flow patterns emerge. These flow patterns can potentially explain the spatial localization/segregation of membrane proteins in processes such as cell polarization. We also identify the relevant parameters that control membrane homeostasis and derive the range of parameters for which homeostatic states exist.