Recent advances in the standardization of 4G cellular networks introduce the notion of multi-coverage, where multiple base stations may collaboratively satisfy the demands of mobile users. We provide a theoretical model for studying such multi-coverage environments, in highly heterogeneous settings, where users demands and profits may vary, as can base stations' capacities and the rates with which they can service the users.Whereas previous works provided solutions that were only applicable to scenarios where rates are uniform throughout the network, or allowed a mobile user to be serviced by at most one base station, we present several algorithms for the multi-coverage problem in the presence of non-uniform rates, and analyze their performance. We complete our study by a simulation study that further validates our results and provides further insight into algorithm design, depending on the users' characteristics.