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The unsourced multiple access channel (MAC) model was originally introduced to study the communication scenario in which a number of devices with low-complexity and low-energy wish to upload their respective messages to a base station. In the original problem formulation, all devices communicate using the same information rate: this may be very inefficient in certain wireless situations with varied channel conditions, power budgets, and payload requirements at the devices. This paper extends the original problem setting to allow for heterogeneous transmissions. More specifically, we consider the scenario in which devices are clustered into two classes with different signal-to-noise ratio (SNR) levels and payload requirements. In the cluster with higher power, devices transmit using a two-layer superposition modulation. In the cluster with lower energy, users transmit with the same base constellation as in the high power cluster. Within each layer, devices employ the same codebook. At the receiver, signal groupings are recovered using Coded Compressed Sensing (CCS) decoder. An outer code is further employed to stitch fragments together across times and layers, as needed. This pragmatic approach to heterogeneous CCS is validated numerically and design guidelines are identified.