Aghion et al. (2007) developed a dynamic bargaining model that considers bilateral versus multilateral trade agreements. Employing a ‘Nash in Nash’ applied general equilibrium framework, we provide empirical evidence for their approach. Considering the Trans-Pacific Partnership (TPP), our model determines the welfare maximizing set of bilateral trade agreements by sectors (there are ten) and compares that to an agreement involving all countries/sectors. We find that a multilateral agreement generates more collective welfare than most bilateral agreements and that this welfare gain is unlikely to be achieved by countries’ individual pursuit of bilateral agreements. We find that superadditivity (i.e., additional welfare associated with the expansion of free trade to additional sectors and countries) holds across all regions and all sectors, but not for every pair of regions and sectors. Thus, it is possible for a set of regions to increase their collective welfare by excluding some sectors from their trade agreement.