Brain tumour segmentation plays a key role in computer-assisted surgery. Deep neural networks have increased the accuracy of automatic segmentation significantly, however these models tend to generalise poorly to different imaging modalities than those for which they have been designed, thereby limiting their applications. For example, a network architecture initially designed for brain parcellation of monomodal T1 MRI can not be easily translated into an efficient tumour segmentation network that jointly utilises T1, T1c, Flair and T2 MRI. To tackle this, we propose a novel scalable multimodal deep learning architecture using new nested structures that explicitly leverage deep features within or across modalities. This aims at making the early layers of the architecture structured and sparse so that the final architecture becomes scalable to the number of modalities. We evaluate the scalable architecture for brain tumour segmentation and give evidence of its regularisation effect compared to the conventional concatenation approach.