Hello. I need some language help.

1)"He is ready to cooperate with authorities, especially with the public prosecutor." Is the second "with" a must or is it possible to do without it: "to cooperate with authorities, especially the public prosecutor"?
2)Is it possible to use "particularly" in the same context (with or without "with"): "to cooperate with authorities, particularly (with)the prosecutor"?
3)Is it possible to use "specifically" in the same context: "to cooperate with authorities, specifically (with?) the prosecutor"?
4)Is it possible to say "to cooperate with authorities, personally with the prosecutor", maybe "to cooperate with authorities, the prosecutor personally".
Thank you for your help.

1. It's clearer if you keep "with" in there.

2. Yes, but be sure to include "with." This is for clarity, to make sure there's no confusion.

3. Yes.

4. No.

Using "with" or not using it affects your reader's ability to understand precisely what you mean.