We investigate a multi-market Cournot model with strategic process research and development (R&D) investments wherein a multi-market firm meets new competitors that enter one of the markets. We show that entry can enhance the total R&D expenditures of the multi-market firm. Moreover, the incumbent's profit nonmonotonically changes as the number of entrants increases. Depending on the fixed entry costs and R&D technologies, both insufficient and excess entry can appear. Our results imply that diversification of their products can be a useful strategy for firms.