From there the conventional First Move turns the lady back so they are side by side again. However, if instead of turning the lady back a full 180º, the man instead turns her only 90º and turns himself 90º, then we have a closed position.
From here lots of possibilities open up, including penguins, pivots, columbians, "basic dips" (which aren't actual dips), etc...
So, yes, the First Move changes when adding things to it, but not significantly.
There is another way to get into a slightly more open closed position from the first move, one which is ideal for doing Manhattans and such, and that is for the man to follow the lady as he turns her out so he is facing her, in the closed position, man's left foot forward, lady's right foot back.
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