This work examines the vulnerability of multimodal (image + text) models to adversarial threats similar to those discussed in previous literature on unimodal (image- or text-only) models. We introduce realistic assumptions of partial model knowledge and access, and discuss how these assumptions differ from the standard "black-box"/"white-box" dichotomy common in current literature on adversarial attacks. Working under various levels of these "gray-box" assumptions, we develop new attack methodologies unique to multimodal classification and evaluate them on the Hateful Memes Challenge classification task. We find that attacking multiple modalities yields stronger attacks than unimodal attacks alone (inducing errors in up to 73% of cases), and that the unimodal image attacks on multimodal classifiers we explored were stronger than character-based text augmentation attacks (inducing errors on average in 45% and 30% of cases, respectively).