Identifying an atom's local crystal structure is one crucial step in many atomistic simulation analyses. However, many traditional methods are available to only a few limited types of structures, and their performance often relies on manually determined parameters, which may lead to poor classification results in complex material systems. Machine learning models can enhance accuracy and generalizability, but they typically require large amounts of data and computation. This issue could be more severe for deep-learning-based frameworks, especially when confronted with unfamiliar crystal structures. To address this challenge, we propose a lightweight and extendable stacked structure (LESS) classifier, which adopts bond orientational order parameters as features and assembles several efficient machine learning methods as based models. The LESS classifier can recognize a variety of crystal structures, e.g., amorphous, mono, and binary structures, with over 98.8% accuracy on our validation data set, outperforming many current methods even including some deep-learning methods. Our model can also conduct probabilistic classification that aids in the interpretation of atomic structures in complicated environments such as heterogeneous interfaces. Furthermore, when exposed to a completely unknown crystal structure, the LESS framework can efficiently incorporate this new knowledge with generative sampled data from the current model. Overall, our model exhibits great potential as an accurate and flexible atomic structure identification tool featuring high efficiency in both learning and retraining.