The parallel plates geometry is often deemed unsuitable for nonlinear viscoelasticity measurements because the strain field, and thus the nonlinear response, varies across the sample. Although cone-plate and Couette geometries are designed to circumvent this problem by ensuring a uniform strain field, it is not always easy to shape the material to the complex shapes that is required for these geometries. This has motivated the development of techniques to accurately determine the nonlinear stress response using the more convenient plate-plate geometry. Here, we introduce a new approach to obtain this true material response in large amplitude oscillatory shear (LAOS) experiments using the plate-plate geometry. By tracing the Fourier components of the torque response and their derivatives with respect to the maximum applied deformation, we accurately obtain the material's true stress-strain response from parallel plate measurements. The approach does not require any assumptions about the material's viscoelastic behavior. We test our approach experimentally on fibrin biopolymer gels, as well as numerically on a Giesekus model. We confirm in both cases that our approach captures the detailed shape of the true stress response in LAOS measurements. Moreover, we also show that our method is less sensitive to experimental noise present in the data than the previous standard method. Our approach for obtaining the true stress response from parallel plate measurements is directly applicable to measurements on a wide range of solid-like nonlinear materials, including biological networks, tissues, or hydrogels.