A method for communication includes providing multiple chassis. Each chassis includes a plurality of slots, which are arranged in at least an outer tier and a middle tier, and which are configured for insertion therein of respective switches. In at least a first chassis among the multiple chassis, first internal interconnects are connected between the slots in the middle tier and the slots in the outer tier, so as to connect each of the slots in the middle tier to multiple slots in the outer tier. In at least a second chassis among the multiple chassis, second internal interconnects are connected directly between the slots in the outer tier. External interconnects are connected between at least some of the slots in the outer tier of the first chassis and at least some of the slots in the outer tier of the second chassis in order to define a network.