Human rights violations and pressing environmental issues have tainted agricultural trade. The role of international market demand for commodities such as soy in causing those problems is clear, yet they remain mostly unaddressed. Therefore, European countries have led a new global trend on mandatory human rights and environmental due diligence (HREDD), advancing the EU's growing global regulatory ambitions. Here, we analyse the prospects for successful externalisation of Europe's sustainability standards – a ‘Brussels Effect’ – using Brazilian soy as a case. Our analysis exposes how the practice of supply chain divergence (i.e., the segmentation of exports tailored to different consumer requirements) can easily evade policy impacts and negate their additionality where Europe commands a minor market share. To avoid becoming just a niche market in these cases, the EU would need to expand on its actions, (i) engaging with other major consumer countries to export its standards, (ii) doubling down on HREDD's coverage to include financial actors and companies trading with other markets, or (iii) moving beyond ‘do no harm’ policies to adopt more strategically targeted ‘do good’ instruments to counter drivers of deforestation on the landscape level.