Yes, you may apply for all of them at the same time, but cannot accept them all; you will need to make a choice when the placement offer is sent. However, as soon as you complete more than 42 calendar days in any other European institution, European Union (EU) body, EU Agency, EU delegations, EU representations in member states, or working for Members of Parliament (MEPs) or Advocates General at the EU Court of Justice (EUCJ), you will no longer be eligible for the European Commission Blue Book traineeship programme.
Please note that experiences at the Council of Europe, Permanent Representations of Member States in Brussels, European University Institute, European Space Agency (ESA), Europe Direct – Info point (desk), or as EPSO EU Career Ambassador, DG Education and Culture's Erasmus Ambassador, EU Climate Ambassador, Youth Ambassador, Horizon Europe Young Observer are accepted.