Improving the power density of solid oxide fuel cell stacks would significantly enhance this technology for transportation. Using a monolithic structure to downsize the stack dimension offers a key to elevate the power density of solid oxide fuel cell stacks. This innovative design is promising but manufacturing is a challenge. The monolith is co-sintered in one firing step, and the gas channels are formed by burning off sacrificial organic materials. Structure distortion or fracture was observed in post-mortem investigations. In this work a multiscale, multiphysics modelling approach is proposed to describe and resolve this challenge in the debinding process occurring in a monolithic stack, i.e. the burning of organics and transportation of gases through the gradually opening microstructure, as well as the pressure build-up in the microstructure due to gas development. Simulation results show that a prominent pressure peak is experienced in the stack when a plasticiser (polyethylene glycol) and a pore-former (polymethyl methacrylate) are decomposed simultaneously. To reduce the high pressures, we investigate two possible strategies: (i) changing the mixture of organic additives; (ii) modifying the debinding temperature profile. Three tapes with different pore-formers are prepared, and the generated pressures during debinding of the three stacks are compared. The corresponding stack shapes after debinding are recorded. Numerical investigations show a good agreement with the post-mortem observations. By changing the composition of organics the distortion or fracturing of the stack can be avoided. Furthermore, to facilitate stack manufacturing, the high pressures can also be reduced by adjusting the heating rates and dwell temperatures of debinding. By using the new temperature profile suggested by the simulation study, the duration of debinding can also be reduced.