An "alien club" was a proposed group consisting of Supergirl, E.T., and the Twelfth Doctor.
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During the filming of Meet That Hero!, after E.T. presented Supergirl with a Kryptonian singing flower that he had used his special abilities to grow, Supergirl suggested the formation of an "alien club". The Twelfth Doctor was enthusiastic about the idea, and offered the help of his TARDIS. (WC: Supergirl Meets E.T.)