Integrated sensing and communication (ISAC) has been recognized as one of the key technologies for future wireless networks, which potentially need to operate in multiple frequency bands to satisfy ever-increasing demands for both communication and sensing services. Motivated by this, we consider the sum sensing rate (SR) optimization for a cooperative ISAC system with linear precoding, where each base station (BS) works in a different frequency band. With this aim, we propose an optimization algorithm based on the semi-definite rank relaxation that introduces covariance matrices as optimization variables, and we apply the inner approximation (IA) method to deal with the nonconvexity of the resulting problem. Simulation results show that the proposed algorithm increases the SR by approximately 25 % and 40 % compared to the case of equal power distribution in a cooperative ISAC system with two and three BSs, respectively. Additionally, the algorithm converges in only a few iterations, while its most optimal implementation scenario is in the low power regime.