Alzheimer's disease is one of the leading causes of dementia worldwide, and its increasing prevalence presents significant diagnostic and therapeutic challenges, particularly in an aging population. Current diagnostic methods, including patient history reviews, neuropsychological tests, and MRI scans, often fail to achieve adequate sensitivity and specificity levels. In response to these challenges, this study introduces an advanced convolutional neural network (CNN) model that combines ResNet-50 and Inception V3 architectures to classify, with a high degree of precision, the stages of Alzheimer's disease based on MRI. The model was developed and evaluated using data from the Alzheimer's Disease Neuroimaging Initiative (ADNI) and classifies MRI scans into four clinical categories representing different stages of disease severity. The evaluation results, based on the precision, sensitivity and F1 score metrics, demonstrate the effectiveness of the model. Additional augmentation techniques and differential class weighting further enhance the accuracy of the model. Visualization of results using the t-SNE method and the confusion matrix underscores the ability to distinguish between disease categories, supporting the model's potential to aid in neurological diagnosis and classification.