Learn English – not only but also + negative sentence

I'd argue that the original sentence is valid.

At the office, it is important not only to look good and fit in; it's also unusual for men and women to outdress their coworkers.

In my opinion, the semicolon here makes the difference; there are now two separate clauses: one that says [paraphrasing] "looking good and fitting in is not the only important thing at the office" and another that says "it is unusual to attempt to outdress your coworkers". In essence, the sentence has used the words "not only" and "also" but is not necessarily a "not only... but also" construct.

I think your rephrasing is a little more confusing.

Perhaps a better way to phrase the sentence would be:

At the office, it is important to look good and fit in; but note that it is unusual for men and women to try to outdress their coworkers.

I would rephrase the sentence as

He likes not only football but also tennis

in the style of the first of the examples here. This rephrasing avoids repeating the verb after but also if it is the same verb that came before the not only (compare with the second example in the link, where there are two different verbs).

Note that here the not only... but also... construction is used to amplify the object of the sentence, which essentially is of the form "He likes THIS". That's why it is not necessary to repeat neither the verb "like" nor the subject "he" inside the object.