In recent years, use of postconsumer recycled (PCR) plastics in asphalt mixes has been gaining popularity owing to increased environmental awareness, and the need to promote sustainability and conserve natural resources. When using the dry process, incorporation of PCR plastic in asphalt mixes poses several challenges, including mixing, sample preparation, and testing. Use of balanced mix design (BMD) for asphalt mixes containing PCR plastic poses additional challenges that have not been adequately covered in previous studies. To this end, changes in the volumetric properties and performance of PCR plastic-modified asphalt mixes were investigated in this study. For this purpose, an asphalt mix having a nominal maximum aggregate size (NMAS) of 9.5 mm and PG 64-22 binder was designed using the BMD approach. Three different percentages (0.25%, 0.5%, and 1% by weight of aggregate) and two different PCR plastics, namely low-density polyethylene (LDPE) and linear low-density polyethylene (LLDPE) were incorporated in the mix using the dry process. Volumetric properties, namely maximum theoretical specific gravity, bulk specific gravity, voids in mineral aggregate, voids filled with asphalt, air void contents, and densities were determined for both control- (0% plastic) and modified mixes. Also, indirect tensile strength, indirect tensile asphalt cracking test, and Hamburg Wheel Tracking tests were performed to assess the performance of these mixes. A comparison of performance for both plastic type and amount and issues related to the incorporation of PCR plastic using the dry process are discussed in this paper.