Numerous automatic sleep stage classification systems have been developed, but none have become effective assistive tools for sleep technicians due to issues with generalization. Four key factors hinder the generalization of these models are instruments, montage of recording, subject type, and scoring manual factors. This study aimed to develop a deep learning model that addresses generalization problems by integrating enzyme-inspired specificity and employing separating training approaches. Subject type and scoring manual factors were controlled, while the focus was on instruments and montage of recording factors. The proposed model consists of three sets of signal-specific models including EEG-, EOG-, and EMG-specific model. The EEG-specific models further include three sets of channel-specific models. All signal-specific and channel-specific models were established with data manipulation and weighted loss strategies, resulting in three sets of data manipulation models and class-specific models, respectively. These models were CNNs. Additionally, BiLSTM models were applied to EEG- and EOG-specific models to obtain temporal information. Finally, classification task for sleep stage was handled by ‘the-last-dense’ layer. The optimal sampling frequency for each physiological signal was identified and used during the training process. The proposed model was trained on MGH dataset and evaluated using both within dataset and cross-dataset. For MGH dataset, overall accuracy of 81.05 %, MF1 of 79.05 %, Kappa of 0.7408, and per-class F1-scores: W (84.98 %), N1 (58.06 %), N2 (84.82 %), N3 (79.20 %), and REM (88.17 %) can be achieved. Performances on cross-datasets are as follows: SHHS1 200 records reached 79.54 %, 70.56 %, and 0.7078; SHHS2 200 records achieved 76.77 %, 66.30 %, and 0.6632; Sleep-EDF 153 records gained 78.52 %, 72.13 %, and 0.7031; and BCI-MU (local dataset) 94 records achieved 83.57 %, 82.17 %, and 0.7769 for overall accuracy, MF1, and Kappa respectively. Additionally, the proposed model has approximately 9.3 M trainable parameters and takes around 26 s to process one PSG record. The results indicate that the proposed model demonstrates generalizability in sleep stage classification and shows potential as a feasibility tool for real-world applications. Additionally, enzyme-inspired specificity effectively addresses the challenges posed by varying montage of recording, while the identified optimal frequencies mitigate instrument-related issues.