When an ion beam is injected into a tapered insulating capillary, the induced self-organized radial Coulomb potential in the capillary is able to focus the beam like an electrostatic lens. However, because of the continued accumulation of charge in the capillary, an equilibrium is rarely attained and the injected beam is eventually Coulomb blocked by the capillary's potential. We propose an original add-on to the capillary setup, which can be tested experimentally and which is expected to hinder the Coulomb blocking. We investigate numerically the benefits and limits of the modified capillary setup. We show how the intensity and emittance of the injected beam control the transmission rate through conically tapered capillaries. Our results indicate that the add-on succeeds to stabilize the asymptotic transmission rate for a larger range of beam intensities and emittances, while reaching a near optimal transmitted fraction up to 90%.