The phrase "also for the second" is correct and usable in written English.
It can be used when referring to an additional point or item that is the second in a series or list.
Example: "We have completed the first phase of the project, and we are now ready to move on also for the second."
Alternatives: "additionally for the second" or "likewise for the second".
The hashtag #OscarsSoWhite began trending worldwide – also for the second year in a row.
Then she was named to the Associated Press all-American first team, also for the second straight year.
He wanted to drop the S sound from the village's name and call it simply Attend -- to wait, not only for work, the preacher explained, but also for the Second Coming.
And mostly for the first reason, but also for the second, said Mr. Imperato (pronounced Im-per-AH-to), he and his father, who is now semi-retired, were looking for a way to stay afloat by the late 1980's.
In the fourth, facing the top of the order again, he struck out Kubek swinging, with a dipping curve that seemed to bounce on the ground in front of Roseboro, and got Richardson out on another big changeup curve; when he fanned Tresh, also for the second time, for his ninth strikeout, the men around me cried "Wow!" in unison.
Alan Pardew could find little to criticise his side for, and there was justification in that, not just for the fact he must lift them for a Premier League campaign in danger of spiralling out of control, and also for the second leg, at what should still be a boisterous St James Parkk next Thursday.
Increasingly, it looks like they could miss out on qualifying again, and not only for the Champions League but also for the second-tier competition, known as the Europa League.
The magazine is also, for the first time, rather stylish.
Also, for the first time, people's eligibility for services will be the same across England.
The Nasdaq composite index closed below 1,800 on Thursday, also for the first time since April.
Also, for the first time, smartphones beeped and buzzed with the alert.
