This article introduces an approach to expanding a stratified sample design, D1, with one primary sampling unit (PSU) selected per stratum to a larger design, D2. Define a workload (WL) to be the sample size in a given stratum in D1. The three-stage approach selects the number of WL's for each stratum, the PSUs to receive additional WLs in each stratum, and the ultimate sampling units. Procedures are given for selecting PSUs in the key second stage, satisfying the following conditions when a stratum in D2 is to have s>=2 WLs: (i) the expected number of WLs in a PSU is s time the probability that it was selected to get the single WL in D1, and (ii) the actual number of WLs assigned is within one of the expected number. These conditions are a generalization of probability proportional to size, without replacement sampling. The properties and variances of this approach are compared to those from three alternative expansion procedures via application to a proposed, but since cancelled, expansion of the Current Population Survey.