Identifying effective therapeutic drug combinations that modulate complex signaling pathways in platelets is central to the advancement of effective anti-thrombotic therapies. However, there is no systems model of the platelet that predicts responses to different inhibitor combinations. We developed an approach which goes beyond current inhibitor-inhibitor combination screening to efficiently consider other signaling aspects that may give insights into the behaviour of the platelet as a system. We investigated combinations of platelet inhibitors and activators. We evaluated three distinct strands of information, namely: activator-inhibitor combination screens (testing a panel of inhibitors against a panel of activators); inhibitor-inhibitor synergy screens; and activator-activator synergy screens. We demonstrated how these analyses may be efficiently performed, both experimentally and computationally, to identify particular combinations of most interest. Robust tests of activator-activator synergy and of inhibitor-inhibitor synergy required combinations to show significant excesses over the double doses of each component. Modeling identified multiple effects of an inhibitor of the P2Y12 ADP receptor, and complementarity between inhibitor-inhibitor synergy effects and activator-inhibitor combination effects. This approach accelerates the mapping of combination effects of compounds to develop combinations that may be therapeutically beneficial. We integrated the three information sources into a unified model that predicted the benefits of a triple drug combination targeting ADP, thromboxane and thrombin signaling.