A variety of architectures have been designed or repurposed for the task of facial forgery detection. While many of these designs have seen great success, they largely fail to address challenges these models may face in practice. A major challenge is posed by generality, wherein models must be prepared to perform in a variety of domains. In this paper, we investigate the ability of state-of-the-art facial forgery detection architectures to generalize. We first propose two criteria for generality: reliably detecting multiple spoofing techniques and reliably detecting unseen spoofing techniques. We then devise experiments which measure how a given architecture performs against these criteria. Our analysis focuses on two state-of-the-art facial forgery detection architectures, MesoNet and XceptionNet, both being convolutional neural networks (CNNs). Our experiments use samples from six state-of-the-art facial forgery techniques: Deepfakes, Face2Face, FaceSwap, GANnotation, ICface, and X2Face. We find MesoNet and XceptionNet show potential to generalize to multiple spoofing techniques but with a slight trade-off in accuracy, and largely fail against unseen techniques. We loosely extrapolate these results to similar CNN architectures and emphasize the need for better architectures to meet the challenges of generality.