Previous studies have shown disparities in health conditions and behaviors among different ethnic groups. Sampling designs that do not consider oversampling certain minority populations, such as American Indians or African Americans, may not produce sufficient sample sizes for estimating health parameters for minority populations. Oversampling is one of the most common approaches that researchers use to achieve required precision levels for small domain estimation. However, it has not been rigorously investigated in dual-frame survey settings. To take advantage of extra information for minority populations in the Marketing Systems Group database, we propose a novel optimal oversampling strategy that minimizes the domain variance subject to total cost restriction or vice versa. We further extend the method to oversample multiple minorities simultaneously. Empirical study using a population-based community survey shows the benefits of our proposed methods compared with traditional methods in terms of statistical efficiency and cost balance.