This paper jointly analyses two major challenges of the canonical NOEM model: i) combining a relatively important exchange rate pass-through at the border with low pass-through at the consumer level, and ii) generating significant endogenous international business cycle synchronization. These issues have been separately analysed in the literature, with extension of the NOEM with a distribution sector for mitigating the exchange-rate pass-through, and foreign input trade for spillovers. We show that introducing input trade for price-maker firms rehabilitate the model regarding the pass-through disconnect, which is especially helpful to model very open economies, while adding a distribution sector lacks flexibility to do so. Moreover, these two extensions of the canonical model mitigate the expenditure switching effect, with implications in terms of international synchronization.