Examples of using "どうぞどうぞ。" in a sentence and their english translations:
By all means.
"May I use your dictionary?" "By all means."
"May I use your telephone?" "By all means."
"May I use the phone?" "Please feel free."
"Do you mind my borrowing your microscope?" "No, not at all."
"Do you mind if I smoke?" "Not at all. Go ahead."
"Do you mind if I call on you sometime?" "No, not at all."