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Frontex is exactly such kind of a unified EU border force[1][2][3]. They occasionly use forced "pushbacks"[4] on migrant boats on Southern sea borders, leading to a lot of criticism and accusations of EU lawbreaking.

[1] https://frontex.europa.eu/

[2] https://en.wikipedia.org/wiki/European_Border_and_Coast_Guar...

[3] https://www.euronews.com/2021/04/27/eu-plans-to-boost-power-...

[4] https://www.euronews.com/2021/01/20/eu-migration-chief-urges...