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.