Telescope Array (TA) is the largest ultrahigh energy cosmic-ray (UHECR) observatory in the Northern Hemisphere. It explores the origin of UHECRs by measuring their energy spectrum, arrival-direction distribution, and mass composition using a surface detector (SD) array covering approximately 700 km$^2$ and fluorescence detector (FD) stations. TA has found evidence for a cluster of cosmic rays with energies greater than 57 EeV. In order to confirm this evidence with more data, it is necessary to increase the data collection rate.We have begun building an expansion of TA that we call TAx4. In this paper, we explain the motivation, design, technical features, and expected performance of the TAx4 SD. We also present TAx4's current status and examples of the data that have already been collected. Comment: 26 pages, 17 figures, submitted to Nuclear Inst. and Methods in Physics Research, A