We develop a model of R\&D collaboration in which individual firms carry out in-house research on core activities and undertake bilateral joint projects on non-core activities with other firms. We develop conditions on the profit functions of the firm under which R\&D investments in different projects of a firm are complementary.We show that this condition is met by standard price and quantity setting oligopoly models. We then study the relation between the number of joint projects and investments and profits. In this context, we identify a second aspect of complementarity: Equilibrium investments in in-house as well as in each joint project are increasing in the number of projects. However, we find that an increase in number of joint projects of all firms lowers collective profits, suggesting the presence of excessive incentives for conducting research.