Computing author intent from multimodal data like Instagram posts requires modeling a complex relationship between text and image. For example, a caption might evoke an ironic contrast with the image, so neither caption nor image is a mere transcript of the other. Instead they combine-via what has been called meaning multiplication Bateman (2014)-to create a new meaning that has a more complex relation to the literal meanings of text and image. Here we introduce a multimodal dataset of 1299 Instagram posts labeled for three orthogonal taxonomies: the authorial intent behind the image-caption pair, the contextual relationship between the literal meanings of the image and caption, and the semiotic relationship between the signified meanings of the image and caption. We build a baseline deep multimodal classifier to validate the taxonomy, showing that employing both text and image improves intent detection by 9.6% compared to using only the image modality, demonstrating the commonality of nonintersective meaning multiplication. The gain with multimodality is greatest when the image and caption diverge semiotically. Our dataset offers a new resource for the study of the rich meanings that result from pairing text and image.