This paper develops a Schumpeterian growth model with overlapping intellectual property rights to analyze the effects of patent protection that features two policy instruments: patent breadth and the profit-division rule between sequential innovators. The former determines the markup and profits of firms, whereas the latter determines the degree to which a patent blocks the subsequent invention. Elastic labor supply and subsidies for intermediate goods and research are also considered. The main results are as follows. First, patents and subsidies are substitutable in eliminating the distortions of this model. Second, given the limited use of subsidies in practice, we study optimal patent protection with exogenous subsidies and derive the coordination of patent instruments attaining the social optimum. Third, optimizing only the profit-division rule retains the first-best R&D level and growth rate, but optimizing only patent breadth could lead to under- or over-investment in R&D; either of these cases is less welfare-enhancing than optimizing their mix. Finally, the model is calibrated to quantify the welfare gains from the decentralized equilibrium to the outcomes with the optimal patent instrument(s), and these welfare improvements can be substantially large. Hence, this study sheds some light on the optimal design and welfare implications of a patent system that is multidimensional and blocks future innovations.