Neural network-based treatment effect estimation algorithms are well-known in the causal inference community. Many works propose new designs and architectures and report performance metrics over benchmarking data sets, in a Machine Learning manner. Nevertheless, most authors focus solely on binary treatment scenarios. This is a limitation, as many real-world scenarios have a multivalued treatment. In this work, we present a novel approach where we generalize a top-performing, neural network-based algorithm for binary treatment effect estimation to a multi-valued treatment setting. Our approach yields an estimator with desirable asymptotic properties, that delivers very good results in a wide range of experiments. To the best of our knowledge, this work is opening ground for the benchmarking of neural network-based algorithms for multi-valued treatment effect estimation.