Multi-source exchangeability models (MEMs) are a Bayesian approach for integrating multiple supplemental data sources into analysis of a primary source. Compared to other Bayesian strategies, they can achieve higher posterior precision with exchangeable sources and significant bias reduction with heterogeneous sources. MEMs were designed to integrate small numbers of supplementary studies, but their model space grows exponentially with the number of sources, and they become intractable for higher-dimensional applications where sources could number in the hundreds or thousands. We propose the iterated MEM (iMEM), which identifies a subset of the most exchangeable sources prior to fitting a final MEM model. We show that iMEM complexity scales linearly with the number of sources and that iMEMs greatly increase posterior precision while maintaining the MEM's desirable asymptotic and small sample properties. We illustrate the application of iMEMs using data from a smartphone application for collecting high-volume individual-level behavior and activity data, resulting in up to 85% increase in efficiency relative to a standard analysis.