grammar - Can the phrase "the likes of which" and "with which" be combined to prevent ending a sentence in a preposition?

Here is the example I was writing when I came across this problem.

It is imperative that you cease this infernal flirtation, lest you unleash forces
the likes of and with which
the world has neither known nor been equipped to contend.

I know there are other ways to phrase this and I'm not militantly opposed to ending sentences in prepositions, but I am interested in the grammatical legitimacy of appending the the word "which" a single time to complete both phrases ("the likes of which" and "with which")--similarly to how the word "in" completes two phrases in the sentence

"I am both interested and involved in the study of linguistic features."

My case is obviously different, since a single word cannot complete both phrases (at least as they are commonly used). The following phrase

"the world has neither known nor been equipped to contend"

must be included to keep the overall statement coherent. But is it grammatical? I was also considering the fact that the word "both" might be what changes my second example ("both interested and involved in"). If the word "both" were added to my original paragraph as follows:

It is imperative that you cease this infernal flirtation, lest you
unleash forces
both
the likes of and with which
the world has neither known nor been equipped to contend.

Would this change anything? I'm sorry if this seems like a pointless question, but I'm seeking out edge cases for a Natural Language algorithm (they are harder to generate than I thought) and I have to seize upon them when I can.

Thanks in advance for your consideration.

Answer

It is imperative that you cease this infernal flirtation, lest you
unleash forces the likes of and with which the world has neither known
nor been equipped to contend.

First, you have a parallelism problem. When you are applying a parallel structure, which is what you're doing, it all has to still work even if you remove parallel parts. While "lest you unleash forces with which the world has not been equipped to contend" makes sense, "lest you unleash forces with which the world has not known" doesn't.

Now, if the last bit weren't a "neither/nor" but an "and," you maybe could get away with writing "the likes of (which) and with which" in the preceding bit, but only if you the alternatives joined by "and" in the second bit were followed by a comma and the word "respectively" in order to cue to the reader that the former refers only to the previous former and the latter refers only to the previous latter and that both don't refer to both of the previous.

That said, I don't see any way that you can restructure your sentence so that the latter part is an affirmative statement, thus allowing you to use "and" instead of "or" or "nor."

The way to write what you wrote is:

It is imperative that you cease this infernal flirtation, lest you

unleash forces the likes of which the world has not known and with
which the world has not been equipped to contend.

After wading through your original sentence to work out what it is you mean, which no reader should have to do, it becomes clear that "the likes of (which)" pertains only to "the world has (not) known" and "with which" pertains only to "the world has...(not) been equipped." Each does not apply to and does not grammatically work with the other, which is required for you to use the parallel structure you are attempting to use.

https://www.grammarly.com/blog/parallelism/

https://en.wikipedia.org/wiki/Parallelism_(grammar)