In collective decision making bilateral deals can increase or decrease the likelihood of finding compromises, depending on whether such deals have externalities. Positive externalities mean third actors profit from bilateral deals, whereas negative externalities mean bilateral deals hurt third actors. We develop the first model of collective decision making that takes externalities into account. The model computes the expected outcomes of the issues to be decided and construes four coalitions of actors on each pair of issues. Then it searches for a set of alternative expected outcomes, such that no coalition can further increase the payoffs of one of its members, either (i) without decreasing the payoffs of one of its members, or (ii) without decreasing the payoffs of any actor. The Generalized Nash Bargaining Solution is used to pick a single outcome. The model is tested on data from decisions in the European Union.