Three-dimensional Morphable Models (3DMMs) are powerful statistical tools for representing the 3D surfaces of an object class. In this context, we identify an interesting question that has previously not received research attention: is it possible to combine two or more 3DMMs that (a) are built using different templates that perhaps only partly overlap,(b) have different representation capabilities and (c) are built from different datasets that may not be publicly-available? In answering this question, we make two contributions. First, we propose two methods for solving this problem: i. use a regressor to complete missing parts of one model using the other, ii. use the Gaussian Process framework to blend covariance matrices from multiple models. Second, as an example application of our approach, we build a new head and face model that combines the variability and facial detail of the LSFM with the full head modelling of the LYHM. The resulting combined model achieves state-of-the-art performance and outperforms existing head models by a large margin. Finally, as an application experiment, we reconstruct full head representations from single, unconstrained images by utilizing our proposed large-scale model in conjunction with the Face-Warehouse blendshapes for handling expressions.