We address multi-item inventory systems with random and seasonally fluctuating, and possibly correlated, demands. The items are produced in two stages, each with its own lead-time; in the first stage a common intermediate product is manufactured. The production volumes in the first stage are bounded by given capacity liits. We develop an accurate lower bound and close-to-optimal heuristic strategies of simple structure. The gap between them, evaluated in an extensive numerical study, is on average only 0.45%. We use the model to investigate the benefits of various delayed product differentiation (postponement) strategies, as well as other strategic questions, including (i) the benefits of flexible versus dedicated production facilities; (ii) the trade-off between capacity and inventory investments; and (iii) the trade-off between capacity investments and service levels.