Interest in forecasting many time series of counts arises in numerous areas, including consumer sales contexts. With a focus on multi-step forecasting of daily sales of supermarket items, we have developed new classes of models based on the concept of decouple/recouple applied to multiple series that are each represented via novel univariate state-space models. The latter involve dynamic generalized linear models for binary and conditionally Poisson time series, random effects for over-dispersion, and covariates in both binary and non-zero count components. New multivariate models enable information sharing across series when aggregated data provide more incisive inferences on shared patterns such as trends and seasonality. These cross-series linkages insulate the parallel estimation of univariate models, hence scaling efficiently in the number of series. A case study on sales of related supermarket items showcases forecasting of multiple series, with discussion of forecast accuracy metrics and probabilistic forecast assessment. Examples demonstrate improved forecast accuracy in a range of metrics, and illustrate the benefits of full probabilistic models for forecasting.