On July 4, 2023, the European Commission (EC) published its proposal for a regulation laying down additional procedural rules for the enforcement of the EU General Data Protection Regulation (GDPR) (proposal). The proposal focuses on procedural issues relating to handling complaints and conducting investigations in cross-border cases.1 The proposal adds to the procedural rules laid down in the GDPR and addresses certain practical issues and gaps. In particular, the proposal harmonizes at an EU-level the rules on complaint admissibility, strengthens due process rights for complainants and defendants, and streamlines cooperation between supervisory authorities (SAs, i.e., national data protection authorities or DPAs). If it is eventually enacted, the proposal would be of considerable importance in facilitating the enforcement of the GDPR in cross-border cases.