The European Commission’s initiative aims to identify and harmonise procedural aspects of cooperation between national data protection supervisory authorities in cross-border cases. To this end, this consultation response presents recommendations that would support the robust enforcement of the GDPR across the European Union, including: specify procedural deadlines for cooperation between data processing agreement (DPAs) on cross-border cases; provide tools to DPAs to promote cooperation early in the investigation process; clarify the position of complainants in the procedural steps; streamline the way parties under investigation are heard during the procedure; and clarify how information is to be shared between the investigating DPA and the concerned supervisory authorities (CSAs).