The clinical effectiveness aspect within the Health Technology Assessment process often faces causal questions where the treatment variable can take multiple values. Nevertheless, most developments in causal inference algorithms that employ machine learning happen in binary treatment settings. In addition, there is a big gap between the algorithmic state of the art and the applied state of the art in this field. In this paper, we select a state-of-the-art, neural network-based algorithm for binary treatment effect estimation and generalize it to a multi-valued treatment setting, testing it with semi-synthetic data that could mimic an HTA process. We obtain an estimator with desirable asymptotic properties and good results in 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.