Driven by the ubiquitous sensing demands, integrated sensing and communication (ISAC) is viewed as an essential technology in future networks. In this paper, we investigate a multiple ISAC-enabled user terminal (UT) system that multi-antenna UTs perform radar sensing and communicate with the BS at the same time. Then, we formulate a multi-UT sum rate maximization problem by jointly considering UT's maximum transmit power and minimum radar signal-to-clutter plus interference and noise ratio (SCINR) requirements. To solve the transmit precoding optimization problem, we first handle the non-convex rate function with weighted minimum mean-squared error method. Then, we use first-order Taylor expansion to deal with the minimum radar SCINR constraints. At last, we propose an iterative optimization algorithm to solve the problem. Simulation results verify the effectiveness of our proposed design.