All these sentences are grammatically correct. This sentence structure is mostly suited to more formal written English, rather than conversation. Conversationally one would say "Please carbon-copy the supervisor (who) you report to", "That's the girl (who) I share/have an intimate relationship with", and so forth.
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victoCan I also say, "My success is due to my friends, of whom I have many."Yes. Again, this feels rather formal.
victoCan I say:Yes. As before, these sentences are more for written English than for conversation.
That is the company with which I am employed.
That is a task for which you are responsible.
victoThat was the task to which you were assigned.This one doesn't work. You are assigned a task, not assigned TO a task.
Grammar GeekHmm. I'm afraid I don't agree with you there, GG.victoThat was the task to which you were assigned.This one doesn't work.
Grammar GeekYou would? Regional variation?I suspect it's more a personal usage differences than a regional variation. I know you can find any old stuff on Google, but I just poked around in Book Search and there seem to be a fairly healthy number of hits for "person assigned to the task", including US publications:
Mr WordyYou are right about not using "whom" for cats.