Why is regulatory convergence towards EU rules more successful in some policy fields than in others within one EU neighboring country? By comparing Ukraine’s convergence towards EU rules in the field of shareholders’ rights and technical standards, I challenge prominent explanations for policy change outside the EU that emphasize misfit and adaptational costs, the institutionalization of EU rules or policy-specific conditionality. In order to deal with the shortcomings of these explanations, it is necessary to disaggregate incentives and capacities of various domestic actors within the particular policy fields. I argue that regulatory convergence in EU neighboring countries is more likely if external actors combine the application of policy-specific conditionality, such as access to the European market, with multiplex capacity-building measures that diversify demand among domestic state regulators and firms and empower them to make their claims.