I was doing practice approaches when I heard approach control contact another aircraft on a similar mission:
"N1234, what are your intentions after this approach?"
"I'll be missed approach, and I'd like vectors to the ILS 36."
"Missed approach instructions: Climb to 2800 and direct to the VOR."
[... sometime later ...]
"Approach, N1234 is missed approach direct to the VOR. Request vectors for the ILS 36."
"Turn right to 1-1-0 degrees, vector for the ILS. Maintain 2800 feet. I'm showing you at 3400 feet."
"Descending to 2800. I'm sorry. I'm having a discussion with the auto-pilot as to which of us is actually pilot-in-command."