Where product innovation requires several complementary patents, fragmented property rights can limit firms' willingness to invest in R&D. We consider the research intensity in multiple simultaneous R&D contests and how it depends on whether firms already hold relevant patents as well as the availability of an option to invent around. A measure of technological uncertainty is also analyzed. The multiple patent product involves an important hold-up problem that can reduce the overall R&D effort. Invent-around options moderate this problem. We also analyze targeted equilibria in which the aim of R&D can be to hold up a rival. Key words: fragmented property rights; patents; contests; hold-up; R&D; inventing around; innovation History: Accepted by Christoph Loch, R&D and product development; received October 12, 2006. This paper was with the authors 5 months for 3 revisions.