The task of sorting spikes from extracellular recordings is pivotal for analyzing meaningful spike trains associated with behavioral responses, stimulation effects, and various other phenomena. This process, however, is significantly challenged by the presence of overlapping spikes, which result from neurons firing either simultaneously or within very short intervals. Such overlapping spikes are frequently disregarded in numerous studies due to the complexities in discerning individual neuronal activities and the lack of a definitive ground truth. In this research, we introduce a novel approach utilizing unsupervised subspace domain adaptation to bridge the gap between real spike subspaces and synthetic spike data, which then serves as the foundation for classifier training. By employing a combination of discriminative subspace learning and isolation forest algorithms, we effectively generate spike templates, subsequently utilizing these to create artificial spikes that help in customizing a classifier specifically designed for this task. Our methodology demonstrates its efficacy in accurately identifying overlapping spikes within simulated datasets, even when solely trained on synthetic data. Moreover, the synergistic application of discriminative subspace learning and isolation forest algorithms significantly enhances the precision of spike template estimation from noisy spike waveforms. The findings from our study propose a cost-efficient and innovative solution for segregating overlapping spikes, employing a heuristic optimization algorithm that could potentially streamline spike sorting processes in neuroscientific research.