The automated classification of stuttered speech has significant implications for timely assessments providing assistance to speech language pathologists. Despite notable advancements in the field, the cases in which multiple disfluencies occur in speech require attention. We have taken a progressive approach to fill this gap by classifying multi-stuttered speech more efficiently. The problem has been addressed by firstly curating a dataset of multi-stuttered disfluencies from open source dataset SEP-28k audio clips. Secondly, employing Whisper, a state-of-the-art speech recognition model has been leveraged by using its encoder and taking the problem as multi label classification. Thirdly, using a 6 encoder layer Whisper and experimenting with various layer freezing strategies, a computationally efficient configuration of the model was identified. The proposed configuration achieved micro, macro, and weighted F1-scores of 0.88, 0.85, and 0.87, correspondingly on an external test dataset i.e. Fluency-Bank. In addition, through layer freezing strategies, we were able to achieve the aforementioned results by fine-tuning a single encoder layer, consequently, reducing the model's trainable parameters from 20.27 million to 3.29 million. This research study unveils the contribution of the last encoder layer in the identification of disfluencies in stuttered speech. Consequently, it has led to a computationally efficient approach, 83.7% less parameters to train, making the proposed approach more adaptable for various dialects and languages.