Pinching antenna systems (PASS) have emerged as a technology that enables the large-scale movement of antenna elements, offering significant potential for performance gains in next-generation wireless networks. This paper investigates the problem of maximizing the average per-user data rate by optimizing the antenna placement of a multi-waveguide PASS, subject to a stringent physical minimum spacing constraint. To address this complex challenge, which involves a coupled fractional objective and a non-convex constraint, we employ the fractional programming (FP) framework to transform the non-convex rate maximization problem into a more tractable one, and devise a projected gradient ascent (PGA)-based algorithm to iteratively solve the transformed problem. Simulation results demonstrate that our proposed scheme significantly outperforms various geometric placement baselines, achieving superior per-user data rates by actively mitigating multi-user interference.