We propose ProtoArgNet, a novel interpretable deep neural architecture for image classification in the spirit of prototypical-part-learning as found, e.g. in ProtoPNet. While earlier approaches associate every class with multiple prototypical-parts, ProtoArgNet uses super-prototypes that combine prototypical-parts into single prototypical class representations. Furthermore, while earlier approaches use interpretable classification layers, e.g. logistic regression in ProtoPNet, ProtoArgNet improves accuracy with multi-layer perceptrons while relying upon an interpretable reading thereof based on a form of argumentation. ProtoArgNet is customisable to user cognitive requirements by a process of sparsification of the multi-layer perceptron/argumentation component. Also, as opposed to other prototypical-part-learning approaches, ProtoArgNet can recognise spatial relations between different prototypical-parts that are from different regions in images, similar to how CNNs capture relations between patterns recognized in earlier layers.