The European Union (EU) has over time developed close relations, typically taking the form of acquis‐based association agreements, with the countries in its Western and Eastern neighbourhood. This article examines when, where and how these non‐Member States can influence the terms of their association with the EU's law and policies via institutional venues. It expands on the literature of external Europeanization and governance, which has mainly focused on the downloading of EU rules by these countries. Yet, the associated neighbours have the opportunity to exert influence at different stages of the law or policy‐making process: first, before the downloading of relevant new rules by uploading or cross‐loading, that is, by attempting to initiate or shape these rules during the agenda‐setting and the formulation phases; and second, during or after the downloading by tweaking or rebuffing relevant new rules in the adoption and implementation phases. These mechanisms of influence at different points in time and in different bodies are illustrated by examples from the countries of the European Free Trade Association, of the Eastern Partnership and in the EU's customs union. The findings indicate that more uploading opportunities can generally be expected, the more downloading is required, and the better the associated countries' access to EU bodies in the early stage of the formulation of new rules. Weak uploading opportunities make joint bodies more important for tweaking and rebuffing. The proposed conceptual framework contributes to the study of external differentiated integration and opens new research avenues.