Does the meaning of "as with" depend on the context?

Question

Initially, I recognized 'as with' as a fixed meaning of 'in the same way as'. But in

In the verbal construction, more follows the head rather than preceding it, as with adjectives and adverbs. Compare, then :It was more enjoyable than usual and I enjoyed it more than usual.

the meaning(in the same way as:) seems not to pass-*preceding it in the same way as adjectives and adverbs. The genuine meaning is 'more follows the head rather than preceding it like preceding adjectives and adverbs.'

In "as with" grammar and meaning in a sentence:

Symbolic logic is a mathematical model of deductive thought; as with other branches of mathematics it has grown beyond the circumstances of its birth.

it too has no 'in the same way as' reading:

As far as it (Symbolic logic) is with other branches of mathematics, it has grown beyond the circumstances of its birth.

But, in

As with other traditional grammarians, Poutsma's most significant classification of adverbials was by meaning, and he indicated that adverbial adjuncts could be divided into those of place, time, causality, and manner.

'as with' here has a 'in the same way as' reading.

So, does the meaning of 'as with' depend on context or the position , introductory or after commas, that 'as with' takes?

Answer 1

In each example, the sense is as is the case with...

The second one says that Symbolic logic has grown beyond the circumstances of its birth, in the same way that other branches of mathematics have done.

Answer 2

with can express the idea of an attendant circumstance.

With certificates of deposit, your money is insured by the government.

Your money is insured by the government with certificates of deposit.

Their being insured by the government is a circumstance that attends them. Being insured "goes along" with them.

See #3 at M-W go along with. That is what I mean by "attends" and "attendant".

You have to be able to handle the stress that attends that kind of difficult work.

"is characteristic of" is another way of expressing the underlying idea of "goes along with" and "attends".

as expresses similarity, a comparison:

As with certificates of deposit, money placed in a checking account is insured by the government.

Money placed in a checking account is insured by the government, as with certificates of deposit.

Paraphrase: Just like [it is] with certificates of deposit, money placed in a checking account is insured by the government.

This notion can be expressed in several ways, including

As is the case with X ....,

Like we see with X, ....