Using overlays in nosys

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I am using nosys to abstract systems in a flake.

According to Overlays - NixOS Wiki there are two ways of using nixpkgs overlays in flakes:

  1. let pkgs = (nixpkgs.legacyPackages.${system}.extend overlay1).extend overlay2

  2. let pkgs = import nixpkgs { inherit system; overlays = [ overlay1 overlay2 ]; }

nosys makes system magically disappear so I seem to be able to get overlays to work in nosys-based flakes using style 1, by removing ${system}.

However, I haven’t managed to adapt style 2 to nosys-based flakes. Can it be done?