I've actually done this.
When operating in the Extra subband from N3ANU (general), I could
either sign with just my callsign (basically, he loaned me his station),
or using N3ANU/WB6BYU (I am control operator at his station).
Not something I do every day, and generally I would just use my
callsign if I was testing their equipment. But there may be cases
where the station callsign is important, such as contact credit for
an award perhaps, or where the other stations in a group would
recognize the station callsign.