Every EU competition that EPSO publishes on its external website is by default open to anyone who meets the formal criteria (including EU officials who may wish to apply to jump to a higher grade, or temporary agents who wish to "finalise" their contract).
On the other hand, EPSO occasionally (usually every 5 years) organises internal competitions which are only open to those already working as permanent or temporary staff at the Commission or other institutions (depending on the exam's specific requirements).
See also:
Notice of Competition, Internal Competition, Staff Regulations
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