Machine learning (ML) has been increasingly used to quantify chemical exchange saturation transfer (CEST) effect. ML models are typically trained using either measured data or fully simulated data. However, training with measured data often lacks sufficient training data, while training with fully simulated data may introduce bias due to limited simulations pools. This study introduces a new platform that combines simulated and measured components to generate partially synthetic CEST data, and to evaluate its feasibility for training ML models to predict amide proton transfer (APT) effect. Partially synthetic CEST signals were created using an inverse summation of APT effects from simulations and the other components from measurements. Training data were generated by varying APT simulation parameters and applying scaling factors to adjust the measured components, achieving a balance between simulation flexibility and fidelity. First, tissue-mimicking CEST signals along with ground truth information were created using multiple-pool model simulations to validate this method. Second, an ML model was trained individually on partially synthetic data, in vivo data, and fully simulated data, to predict APT effect in rat brains bearing 9L tumors. Experiments on tissue-mimicking data suggest that the ML method using the partially synthetic data is accurate in predicting APT. In vivo experiments suggest that our method provides more accurate and robust prediction than the training using in vivo data and fully synthetic data. Partially synthetic CEST data can address the challenges in conventional ML methods.