Esteban and Sakovics (2003) showed in their three-person game that an alliance never appears in a possibly multi-stage contest game for an indivisible prize when allies' efforts are perfectly substitutable. In this paper, we introduce allies' effort complementarity by using a CES effort aggregator function. We consider an open-membership alliance formation game followed by two contests: the one played by alliances, and the one within the winning alliance. We show that if allies' efforts are too substitutable or too complementary, no meaningful alliance appears in equilibrium. However, if allies' efforts are moderately complementary to each other, then competition between two alliances is a subgame perfect equilibrium, which Pareto-dominates the equilibrium in a noalliance single-stage contest. We also show that if forming more than two alliances is supported in equilibrium, then it Pareto-dominates two alliance equilibrium. Nevertheless, the parameter space for such an allocation to be supported as an equilibrium shrinks when the number of alliances increases.