If you are avoiding ending a sentence with prepositions ("That was a situation, in which it was better to not become entangled."), what happens if you use a verb with a preposition? Suppose I wanted to say "This is something we will not put up with." Should I say "This is something with which we will not put up." since put and up form a phrasal verb, or should I say "This is something up with which we will not put"?
The answer is that if you insist on following the nonsensical rule, then you'll have to say up with which we will not put, like the famous example (probably wrongly) attributed to Winston Churchill.
Note that the phrasal verb here is put up with, not put up, which has a number of meanings, all of them different from put up with. For this reason something with which we will not put up, though grammatical, is confusing and likely not to be understood.
The English for these is which we will not put up with.