This paper investigates the maximal achievable multi-rate throughput problem of a multicast session at the presence of network coding. Deviating from previous works which focus on single-rate network coding, our work takes the heterogeneity of sinks into account and provides multiple data layers to address the problem. Firstly formulated is the maximal achievable throughput problem with the assumption that the data layers are independent and layer rates are static. It is proved that the problem in this case is, unfortunately, Non-deterministic Polynomial-time (NP)-hard. In addition, our formulation is extended to the problems with dependent layers and dynamic layers. Furthermore, the approximation algorithm which satisfies certain fairness is proposed.