This paper studies a capacity management problem with upgrading. A firm needs to procure multiple classes of capacities and then allocate the capacities to satisfy multiple classes of customers that arrive over time. A general upgrading rule is considered, i.e., unmet demand can be satisfied using multi-step upgrade. No replenishment is allowed and the firm has to make the allocation decisions without observing future demand. We first characterize the structure of the optimal allocation policy, which consists of parallel allocation and then sequential rationing. We also propose a heuristic based on certainty equivalence control to solve the problem. Numerical analysis shows that the heuristic is fast and delivers close-to-optimal profit for the firm. Finally, we conduct extensive numerical studies to derive insights into the problem. It is found that the value of using multi-step upgrading can be quite significant. However, the firm’s profit is not sensitive in the initial capacity if the optimal upgrading policy is used.