INTRODUCTION: Alzheimer's disease (AD) is one of the most common neurodegenerative disabilities that often leads to memory loss, confusion, difficulty in language and trouble with motor coordination. Although several machine learning (ML) and deep learning (DL) algorithms have been utilized to identify Alzheimer's disease (AD) from MRI scans, precise classification of AD categories remains challenging as neighbouring categories share common features. METHODS: This study proposes transfer learning-based methods for extracting features from MRI scans for multi-class classification of different AD categories. Four transfer learning-based feature extractors, namely, ResNet152V2, VGG16, InceptionV3, and MobileNet have been employed on two publicly available datasets (i.e., ADNI and OASIS) and a Merged dataset combining ADNI and OASIS, each having four categories: Moderate Demented (MoD), Mild Demented (MD), Very Mild Demented (VMD), and Non Demented (ND). RESULTS: Results suggest the Modified ResNet152V2 as the optimal feature extractor among the four transfer learning methods. Next, by utilizing the modified ResNet152V2 as a feature extractor, a Convolutional Neural Network based model, namely, the 'IncepRes', is proposed by fusing the Inception and ResNet architectures for multiclass classification of AD categories. The results indicate that our proposed model achieved a standard accuracy of 96.96%, 98.35% and 97.13% for ADNI, OASIS, and Merged datasets, respectively, outperforming other competing DL structures. DISCUSSION: We hope that our proposed framework may automate the precise classifications of various AD categories, and thereby can offer the prompt management and treatment of cognitive and functional impairments associated with AD.