A number of procedures have been developed, beginning with the work of Keyfitz, for maximizing or minimizing the overlap of sampling units for two stratified designs. Most of these procedures are not applicable at all, or are not feasible to implement, unless the number of units selected per stratum is very small. The author previously presented a procedure for increasing or decreasing overlap when a large number of units per stratum are selected and when the sample units for the two designs must be selected sequentially, as is the case when the second design is a redesign of the first design. That procedure does not generally yield an optimal overlap. In the current paper a very different large sample per stratum procedure is presented for maximizing or minimizing overlap when the units can be selected for the two designs simultaneously, as may be the case for two different surveys. The procedure guarantees an optimal overlap if the two designs have identical stratifications, but can still be used, with loss of optimality, if the stratifications differ. An application of this procedure to the joint selection of samples for two BLS compensation surveys is discussed.