Structured Illumination Microscopy is a widespread methodology to image live and fixed biological structures smaller than the diffraction limits of conventional optical microscopy. Using recent advances in image up-scaling through deep learning models, we demonstrate a method to reconstruct 3D SIM image stacks with twice the axial resolution attainable through conventional SIM reconstructions. We further evaluate our method for robustness to noise & generalisability to varying observed specimens, and discuss potential adaptions of the method to further improvements in resolution.