Supplemental samples are used in surveys to increase sample sizes when there is a low response rate or high ineligibility. There are no straightforward methods for drawing supplemental samples for a systematic probability proportional to size (PPS) sample design after the main sample had been selected. We examine a situation where there was a large number of ineligible in the sampling frame, which were known after the main sample was selected but before drawing the supplemental sample. A non-overlapping supplemental sample was drawn by randomly offsetting the random start of the main sample interval. We discuss several methods for creating the base and replicate weights that properly reflect the variance estimates for this design. The methods include the inverse of the probability of selection, the expected probability of selection, assuming double sampling, post-stratification to eligible totals, and estimating the probability of selection through simulation. We also evaluate the replicate weights created using either the realized sample or the combined main and supplemental samples. We compare the empirical bias and variance for these methods using Monte Carlo simulations.