We consider an overlaid broadcast service, where a spread spectrum (SS)-based broadcast signal is overlaid onto the existing terrestrial Digital Multimedia Broadcasting (T-DMB) band. The system is similar to the augmented data transmission in the ATSC DTV, for which it was investigated mostly in terms of link level performance, such as bit error rate. Our focus in this paper is on the system-level performances. More specifically, utilizing both a large scale path loss and a small scale fading channel model, the primary objective is to explore the tradeoff between the coverage and the achievable rate of the overlaid service and, finally, to determine the achievable rate in the overlaid service for marginal coverage reduction in the existing broadcast service. The analytical and simulation results show that an SS-based add-on service of 10 kbps to 20 kbps can co-exist with the T-DMB service while resulting in only a marginal degradation in T-DMB coverage (for example, less than one percent reduction).