We present new methodology and a case study in use of a class of Bayesian predictive synthesis (BPS) models for multivariate time series forecasting. This extends the foundational BPS framework to the multivariate setting, with detailed application in the topical and challenging context of multi-step macroeconomic forecasting in a monetary policy setting. BPS evaluates – sequentially and adaptively over time – varying forecast biases and facets of miscalibration of individual forecast densities for multiple time series, and – critically – their time-varying interdependencies. We define BPS methodology for a new class of dynamic multivariate latent factor models implied by BPS theory. Structured dynamic latent factor BPS is here motivated by the application context – sequential forecasting of multiple US macroeconomic time series with forecasts generated from several traditional econometric time series models. The case study highlights the potential of BPS to improve of forecasts of multiple series at multiple forecast horizons, and its use in learning dynamic relationships among forecasting models or agents.