© 2018 The Author(s). Accurate diagnosis of mild cognitive impairment (MCI) before conversion to Alzheimer's disease (AD) is invaluable for patient treatment. Many works showed that MCI and AD affect functional and structural connections between brain regions as well as the shape of cortical regions. However, 'shape connections' between brain regions are rarely investigated -e.g., how morphological attributes such as cortical thickness and sulcal depth of a specific brain region change in relation to morphological attributes in other regions. To fill this gap, we unprecedentedly design morphological brain multiplexes for late MCI/AD classification. Specifically, we use structural T1-w MRI to define morphological brain networks, each quantifying similarity in morphology between different cortical regions for a specific cortical attribute. Then, we define a brain multiplex where each intra-layer represents the morphological connectivity network of a specific cortical attribute, and each inter-layer encodes the similarity between two consecutive intra-layers. A significant performance gain is achieved when using the multiplex architecture in comparison to other conventional network analysis architectures. We also leverage this architecture to discover morphological connectional biomarkers fingerprinting the difference between late MCI and AD stages, which included the right entorhinal cortex and right caudal middle frontal gyrus.