The combination of log-likelihood ratio (LLR) quantization and network coding was previously shown to be a promising compress-and-forward strategy for the multiple access relay channel with two sources. In this paper, we generalize this approach to the case of more than two sources. Our proposed relay scheme consists of a scalar LLR quantizer for each source followed by a network coding (NC) step that suitably combines the quantizer outputs. We use the information bottleneck method to design the quantizers and the NC function. At the destination, an iterative message-passing decoder is used to jointly decode all source messages. Numerical simulations demonstrate the effectiveness of the proposed transmission strategy and its suitability for asymmetric source-relay channel conditions.