The Ultra-fast Transient Experimental Facility (UTEF) at Chongqing University is currently constructing a 500MeV storage ring. This paper investigates the transverse coupled-bunch instabilities (TCBI) critical to its high-current operation. Building on a method previously developed at Diamond Light Source—which enables the calculation of all coupled-bunch instability modes within a single simulation—this work extends the approach to non-zero chromaticity cases using a multi-particle-per-bunch model. Results for the UTEF ring demonstrate that non-zero chromaticity and synchrotron radiation damping have a negligible impact on the grow-damp curve. On the other hand, the inclusion of short-range impedance brings an obvious shift of the grow-damp curve. This paper provides a detailed account of the simulation and results.