Drug screening plays a crucial role in the development of innovative therapeutics for various diseases. In this study, we propose a novel approach using probabilistic multi-output models to predict drug response at all doses and uncover their biomarkers. By leveraging genomic features and chemical properties of drugs, our multi-output Gaussian Process (MOGP) models provide a comprehensive understanding of drug efficacy across different dose metrics. This approach was tested across two drug screening studies and five cancer types. It captured underlying response trends and enabled the identification of the EZH2 gene as a novel biomarker of BRAF inhibitor response. We demonstrate the effectiveness of our MOGP models in accurately predicting dose-responses in different cancer types and when there is limited number of drug screening experiments for training. Our findings highlight the potential of MOGP models in enhancing drug development pipelines by reducing data requirements and improving precision in dose-response predictions.