They could be written more formally as:

Who does Kim think the coworkers want management to replace her with?

With whom does Kim think that her coworkers would like management to replace her?

Who does Kim think Carol hopes Jim says the coworkers want management to replace her with?

With whom does Kim think that Carol hopes that Jim says that her coworkers would like management to replace her

The grammar in the formal versions is more closely related to Latin grammar, but it introduces a stiffness into the construction that appears to be a dying trend. Forms that, 20 years ago, would have been considered errors, are now accepted practice and come more easily to the tongue, such as:

Ending a sentence with a preposition: Who ... with as opposed to With whom

The split infinitive: They could be more formally written as... as opposed to They could be written more formally as...

...and I am pleased that it is so. I love the flexibility of English, the fact that it is so adaptable, but it does make parsing it hell!

update jporter correctly pointed out that this is not a split infinitive

Clint

What's considered "acceptable English" almost always says more about the prescriptivists than it does about the language itself. Preposition stranding is perfectly acceptable (and actually preferred) by native speakers, and I don't believe that "who" really has case in English anymore. I often see native speakers attempting to use "whom," but invariably distinguishing "whom" from "who" not in that "whom" has object case but that "whom" is a relativizer:

I like to visit my grandmother whom always gives me delicious cookies. (also see this)

The notion that modern English should adhere to Latin grammar rules is actually quite ridiculous when you think about it: modern English is separated from Latin by a thousand years, and isn't even descended from Latin (English is Germanic). This notion is more attributable to the Western infatuation with everything Classical rather than any property of English itself.

This isn't to say, of course, that standards shouldn't be adopted to try to make English as intelligible as possible to non-native speakers in appropriate circumstances, but these standards should be understood as outside impositions towards maximally helpful language use rather than as characterizations of good language use.

I apologize if this is way too off-topic.

... the prescriptivists ...

Nice. I found a new way to insult all those language snobs I so love to hate :)

---

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.

"Science is about questioning the status quo. Questioning authority".

In the absence of evidence, opinion is indistinguishable from prejudice.

"Too many [] have been sedated by an oppressive environment of political correctness and risk aversion."

Assuming that both questions regard replacing Kim, unless it's known to the audience that Carol is a male (unusual, but not unknown), then "With whom does Kim think that Carol hopes that Jim says that her coworkers would like management to replace her?" is ambiguous, and violates the grammar rules I was taught. Because the antecedent of the pronoun is not the nearest appropriately-gendered noun, one must replace "her" with "Kim" to be painfully correct.

The split infinitive: They could be more formally written as...

That's not a split infinitive, because it's not an infinitive at all. The word rearrangement you suggest has null effect, except perhaps for questions of style.

The thing I don't like about "They could be more formally written as..." is that it's in the passive voice. This could be eliminated by rewording as "One could write them more formally as..." But, of course, there are contexts in which passive voice is not only acceptable but preferable, for example, in scientific writing. Is this discourse scientific enough to merit passive voice? I don't know, but I personally would err on the other side.

A word spoken in Mind will reach its own level, in the objective world, by its own weight