Until recently, all of the procedures developed for maximizing the overlap of sample units for two or more stratified designs with the samples selected sequentially, destroyed the independence of sampling from stratum to stratum for all but the first sample selected, unless the stratifications were identical or variable sample sizes were allowed. This independence is needed to guarantee the validity of the usual variance estimation procedures. Ohlsson (1996, 1999, 2000) has developed a simple overlap procedure, applicable to a wide variety of designs, that preserves this independence. This procedure, which he calls exponential sampling, uses transformed permanent random numbers (PRNs) to select each sample. For situations where exponential sampling has not been used to select the first sample, Ohlsson (1996) has developed a method, for one sample unit per stratum designs only, for retrospectively assigning the PRNs after the initial sample has been drawn and then selecting subsequent samples using these PRNs and exponential sampling. In this paper we generalize this result of Ohlsson by demonstrating how to retrospectively assign PRNs for designs of more than one unit per stratum.