Large multi-product firms dominate international trade flows. Using novel linked production and export data at the firm-product level, we find that the overwhelming majority of manufacturing firms export products that they do not produce. Three quarters of the exported products and thirty percent of export value from Belgian manufacturers are in goods that are not produced by the firm, so-called Carry-Along Trade (CAT). The number of CAT products is strongly increasing in firm productivity while the number of produced products that are exported is weakly increasing in firm productivity. We propose a general model of production and sourcing at multi-product firms and explore new demand- and supply-side modeling features capable of generating predictions consistent with the empirical findings. Export price data and company interviews offer suggestive evidence for the presence of demand-scope complementarities.