We describe a model of international, multidimensional policy coordination where countries can enter into selective and separate agreements with different partners along different policy dimensions. The model is used to examine the implications of negotiation tie-in – the requirement that agreements must span multiple dimensions of interaction – for the viability of multilateral cooperation when countries are linked by international trade flows and transboundary pollution. We show that, while in some cases negotiation tie-in has either no effect or can make multilateral cooperation more viable, in others a formal tie-in constraint can make an otherwise viable joint multilateral agreement unstable.