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The phrase "again after the first" is correct and usable in written English.
It can be used to indicate a repetition of an action or event following an initial occurrence.
Example: "We will meet again after the first session to discuss our progress."
Alternatives: "once more following the initial" or "subsequently after the first".
Exact(27)
"We never thought they'd come again after the first time.
Again, after the first decades of industrialization, reform laws began to respond.
Unless explicitly uncommented, inputs corresponding to the following will not be read in again after the first run.
Obviously not grandpa Ludwig who emigrated to Berlin when Poznan became Polish again after the first world war.
The dining room captain promised not to split us up again after the first night and he kept his word.
Suárez never played for Ajax again after the first biting incident; the club sold him to Liverpool during that winter's January transfer window.
Similar(33)
Participants' knowledge of solar energy was assessed after the first learning experience and then again after the second learning experience.
The particles with the core shell structure were observed again after the second reduction treatment for the reoxidized catalyst.
Patients completed daily diaries on two week-long occasions: after the intake interview and again after the sixth session of CT.
Interestingly, the system returns to the trivial phase once again after the second band inversion at the M-point.
He required medical attention before the fifth set, and again after the third game, for soreness in his upper right hamstring and hip.
More suggestions(13)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com