I propose a new majoritarian bargaining model in which more than one implicit proposal can be on the table at the same time. Institutional differences from system to system affect the order of play, the equilibrium majorities, and the policy outcome. The ex post distribution of payoffs within a winning coalition is, however, invariant to fundamental institutional differences, and it is always proportional to the distribution of relative ex ante bargaining power. The bargaining process is modeled as a sequential demand game, in which players are called to propose a policy and to specify their desired share of the private benefits related to being in office. The order of play is endogenous, and the distribution of payoffs within an equilibrium majority usually does not depend on who is the proposal maker. The role of the head of state and the advantages to center parties are also studied.