The temperature driven rarefied gas flow and the associated pressure difference in a multistage assembly consisting of a series of channels with linearly diverging or converging rectangular cross sections are computationally investigated. Each stage of the multistage assembly is consisting of one converging and one diverging channel. The net mass flow rate and the induced pressure difference between the inlet and outlet of the multistage assembly are parametrized in terms of the geometrical and operational data, paying specific attention to the diode effect and to the number of stages. The flow may be in the whole range of the Knudsen number and therefore modeling is based on kinetic theory, while the channels are taken efficiently long in order to justify the implemented infinite capillary methodology. Various flow setups are investigated to obtain the characteristic curves of the net mass flow rate versus the pressure difference in terms of channel geometry, input pressure, imposed temperature ratio and number of stages. The present work provides a powerful modeling tool in the manufacturing of a multistage Knudsen pump meeting certain pumping specifications.