To have non-zero net flow in AC electroosmotic pumps, the electroosmosis (EO) has to be non-linear and asymmetric. This can be achieved due to ionic concentration polarization. This is known to occur close to micro-/nano-interfaces provided that the sizes of the nanopores are not too large compared to the Debye screening length. However, operation of the corresponding EO pumps can be quite sensitive to the solution concentration and, thus, unstable in practical applications. Concentration polarization of ion-exchange membranes is much more robust. However, the hydraulic permeability of the membrane is very low, which makes EO flows through them extremely small. This communication shows theoretically how this problem can be resolved via making scarce microscopic perforations in an ion-exchange membrane and putting it in series with an EO-active nano-porous medium. The problem of coupled flow, concentration and electrostatic-potential distributions is solved numerically by using finite-element methods. This analysis reveals that even quite scarce perforations of micron-scale diameters are sufficient to observe practically-interesting EO flows in the system. If the average distance between the perforations is smaller than the thickness of the EO-active layer, there is an effective homogenization of the electrolyte concentration and hydrostatic pressure in the lateral direction at some distance from the interface. The simulations show this distance to be somewhat lower than the half-distance between the perforations. On the other hand, when the surface fraction of perforations is sufficiently small (below a fraction of a percent) this “homogeneous” concentration is considerably reduced (or increased, depending on the current direction), which makes the EO strongly non-linear and asymmetric. This analysis provides initial guidance for the design of high-productivity and inexpensive AC electroosmotic pumps.