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We study how firms react to unexpected increases in import tariffs. We identify our results from a sudden removal of American preferential tariffs applied on Argentine imports under the Generalized System of Preferences, which reflected American retaliation to a dispute over intellectual property between the two countries. Critical for identification, the tariff hike affected a third of Argentine exports enjoying preferential access in the American market, but did nothing to the other two thirds. We find that the higher tariffs reduced export participation of affected Argentine firms in the US market, whereas resilient exporters dealt with the cost increase by reshuffling their export baskets away from the products whose tariffs increased. In fact, affected firms were more likely both to drop suspended products from their export basket and to start exporting new (non-suspended) products to the US Interestingly, the extensive margin effects carry over to third markets, where policy did not change: after the policy shock, affected firms selling to the US were less likely to export to other markets. This happened, however, only for firms that also exited the American market. We develop a framework that rationalizes the observed export interdependencies: while the extensive margin and third-country effects require country and product specific fixed costs, the effect on the sub-extensive and sub-intensive margins require diseconomies of scope, where exporting a product increases the marginal cost of exporting the rest of products in the export mix.