Breast cancer is the first new case occurring and the fifth death-causing cancer disease in 2020, which collapses the families as women are the pillar of the family members. 3D image acquisition technology increases treatment methods and decreases the rate of breast cancer death. Furthermore, single-label breast cancer classifications are deployed to solve the problem. However, it cannot convey more information about mammogram images. In the area where the shortage of datasets is there as in the medical image, data augmentation and transfer learning are the best solution. A Multi-Label Breast Cancer Screening is a deep learning model using a transfer learning model that gives information on finding, density, and pathology of patients' breast mammograms to the radiologists, aiming for life-saving and supporting the family. The existing model shows low accuracy on feature extraction and more layers with a very large number of nodes in a layer in the classification part. In this study, the best feature extractor for this particular work is investigated and identified as efficientnetb3, and ONN is used for the classification part. The proposed model outperforms the previous work in all evaluation metrics with a 13.25% f1_score, 53% hamming loss, 36.7% coverage error, and 12.5 an exact match. And , the number of parameters were decreased from 134M to 20M which was resulted from the optimizing of classification part of the model. The developed model with ONN in the classification part has made the best improvement over the existing model in terms of evaluation metrics and network performances.