We present a parts-based 3D Morphable Model (3DMM) of the full human head, with particular emphasis on modelling the complex shape of the ear as a flexible, high-resolution separate part. The 3D ear model part undergoes an iterative process of refinement that employs data augmentation using a 2D image dataset with landmarked ears. Evaluations using several performance metrics validate the training process and the resulting model. We make the new ear model and our reconstructed training dataset publicly available. We merge the trained high-resolution 3DMM of the ear with a publicly-available 3DMM of the full head that has a much lower resolution in the ear regions. The resulting parts-based 3DMM provides more shape variation and more shape detail in the ears, and we demonstrate a higher fidelity overall model fit to raw data.