Classification is a fundamental task in machine learning. While conventional methods-such as binary, multiclass, and multi-label classification-are effective for simpler problems, they may not adequately address the complexities of some real-world scenarios. This paper introduces the Multiplex Classification Framework, a novel approach developed to tackle these and similar challenges through the integration of problem transformation, ontology engineering, and model ensembling. The framework offers several advantages, including adaptability to any number of classes and logical constraints, an innovative method for managing class imbalance, the elimination of confidence threshold selection, and a modular structure. Two experiments were conducted to compare the performance of conventional classification models with the Multiplex approach. Our results demonstrate that the Multiplex approach can improve classification performance significantly (up to 10% gain in overall F1 score), particularly in classification problems with a large number of classes and pronounced class imbalances. However, it also has limitations, as it requires a thorough understanding of the problem domain and some experience with ontology engineering, and it involves training multiple models, which can make the whole process more intricate. Overall, this methodology provides a valuable tool for researchers and practitioners dealing with complex classification problems in machine learning.