The Hierarchy Of Time-Surfaces (HOTS) algorithm, a neuromorphic approach for feature extraction from event data, presents promising capabilities but faces challenges in accuracy and compatibility with neuromorphic hardware. In this paper, we introduce Sup3r, a Semi-Supervised algorithm aimed at addressing these challenges. Sup3r enhances sparsity, stability, and separability in the HOTS networks. It enables end-to-end online training of HOTS networks replacing external classifiers, by leveraging semi-supervised learning. Sup3r learns class-informative patterns, mitigates confounding features, and reduces the number of processed events. Moreover, Sup3r facilitates continual and incremental learning, allowing adaptation to data distribution shifts and learning new tasks without forgetting. Preliminary results on N-MNIST demonstrate that Sup3r achieves comparable accuracy to similarly sized Artificial Neural Networks trained with back-propagation. This work showcases the potential of Sup3r to advance the capabilities of HOTS networks, offering a promising avenue for neuromorphic algorithms in real-world applications.