Breast cancer ranks as the second most common cancer affecting women. Early prediction of breast lesions significantly enhances patient survival rates. In India, however, obtaining an early medical diagnosis poses considerable challenges. Often, by the time the initial screening takes place, the lesion has progressed to a grade 2 or higher level. The classification of different stages of breast lesion histopathology images is a complex task, as it may lead to confusion in interpreting certain lesion images. Most of the existing literature has extensively explored various neural network models for multiclass classification of different stages of breast lesion histopathology images. In such cases, pre-trained deep neural network models have been commonly utilized, but they have yielded comparatively lower accuracy. Therefore, in this paper, we propose a novel approach involving the fine-tuning of the standard Inception V3 model and optimizing hyperparameters for categorizing histopathology breast lesion images stained with the BACH dataset. To enhance the deep neural networks (DNN) performance, several data augmentation techniques are employed. Our proposed network architecture, utilizing the fine-tuned Inception V3 model, achieves an impressive 97% test accuracy, a 76% F1-score, 87% precision, and 80% recall. When compared with recently reported literature, our model exhibits slightly superior performance.