Non-traditional warehouses rise as effective solutions to shorten the travelled distances to store and retrieve unit loads, adding aisles crossing the parallel racks. Multiple warehouse configurations are proposed by the literature discussing the enhancements toward standard layouts. In previous contributions, the authors introduced the diagonal cross-aisle model, concluding about its positive impact on the handling performances under single command operations. This paper extends the previous works, integrating dual command operations, through an original analytic model supporting the design of non-traditional warehouses with a couple of symmetric straight diagonal cross-aisles and random storage assignment strategy. The closed-form expressions to compute the expected cycle travel distances are provided, optimising the aisle position. An industrial case study applies the model, getting distance savings ranging from 11 to 17%, compared to standard layout and further considering the loss of storage space due to the presence of the additional aisles.