The idea that transnational corporations (TNCs) have at least negative duties in relation to human rights is widely accepted among political theorists and practitioners. However, there is still disagreement if corporations also bear positive duties and under which conditions. This paper adds to the current debate and argues that while corporations essentially bear negative duties, i.e. they must respect human rights, these duties are more demanding than current accounts suggest. Most approaches only focus on the harms corporations produce in the course of their activities or to which they contribute through their relationships with other actors. However the proposed approach considers that corporations may also contribute to human rights violations via institutional channels, for example, by shaping and maintaining a global institutional arrangement that predictably gives rise to human rights violations. These contributions, is argued, should be taken into consideration to broaden the scope of TNCs’ duty to respect. In the proposed approach the duty to respect requires corporations avoid violating human rights both directly and via institutional channels. To honour their duty corporations face two options: either stop participating in the institutional order or actively seek to reform it. The first option seems unrealistic as TNCs depend on the existence of a global institutional arrangement to operate. Therefore, even if it is accepted that corporations bear essentially negative duties, there is a case to require from them certain actions that have been traditionally related with positive duties.