A central challenge in every field of biology is to use existing measurements to predict the outcomes of future experiments. In this work, we consider the wealth of antibody inhibition data against variants of the influenza virus. Due to this virus's genetic diversity and evolvability, the variants examined in one study will often have little-to-no overlap with other studies, making it difficult to discern common patterns or unify datasets for further analysis. To that end, we develop a computational framework that predicts how an antibody or serum would inhibit any variant from any other study. We use this framework to greatly expand 7 influenza datasets utilizing hemagglutination inhibition, validating our method upon 200,000 existing measurements and predicting more than 2,000,000 new values along with their prediction uncertainties. This data-driven approach does not require any information beyond each virus's name and measurements, and even datasets with as few as 5 viruses can be expanded, making this approach widely applicable. Future influenza studies using hemagglutination inhibition can directly utilize our curated datasets to predict newly measured antibody responses against ≈80 H3N2 influenza viruses from 1968-2011, whereas immunological studies utilizing other viruses or a different assay only need to find a single partially-overlapping dataset to extend their work. In essence, this approach enables a shift in perspective when analyzing data from "what you see is what you get" into "what anyone sees is what everyone gets."