In blood transfusion studies, its is often desirable before a surgical procedure to estimate the likelihood of a patient bleeding, need for blood products, re-operation due to bleeding and other important patient outcomes. Such prediction rules are crucial in allowing for optimal planning, more efficient use of blood bank resources, and identification of high-risk patient cohort for specific perioperative interventions. The goal of this study is to present a simple and efficient algorithm that could estimate the risk of multiple outcomes simultaneously. Specifically, a heterogeneous multi-task learning method is presented for learning important surgical outcomes such as bleeding, intraoperative RBC transfusion, need for ICU care, length of stay and mortality. To improve the performance of the method, a post-learning strategy is implemented to further learn the relationship between the trained tasks by a simple goodness of fit measure. Specifically, two tasks are considered similar if the model parameters of one tasks improves predictive performance of the other. This strategy allows tasks to be grouped in clusters where selective cross-task transfer of knowledge is explicitly encouraged. To further improve prediction accuracy, a number of operative measurements or surgical outcomes whose predictions are not of direct interest are incorporated in the multi-task model as supplementary tasks to donate information and help the performance of relevant tasks. Results for predicting bleeding and need for blood transfusion for patients undergoing non-cardiac operations from an institutional transfusion datamart show that the proposed methods can improve prediction accuracy over standard single-tasks learning methods. Additional experiments on a real public available data set show that the method is accurate and competitive with some existing methods in the literature.