I would have no concern about giving 8 mg of ondansetron IV. As a matter of fact, I effectively do it all the time when a patient receives 4 mg at the end of the surgery and 15 min later is c/o nausea and I give another 4 mg followed by perhaps 10 mg of metoclopramide. The big boogeyman with ondansetron is QT prolongation, so having a baseline ECG that shows a normal QT interval would be nice before such hefty doses. Slapping a tele box on might not hurt either, but I wouldn't say it's necessary, especially in the patient described in the OP.
Ironically, the same supervisor that was so worried we were going to overdose the patient with Zofran is now saying there is no reason we shouldn't be able to give Fentanyl IVP which I think is a lot more dangerous.
That is hilarious. I give tons of fentanyl and I've seen folks get knocked out and need their chins held with even modest doses. That said, if the patients are terminally ill and opiod tolerant there is no safety reason not to give them fentanyl IVP on the floor. I would question why fentanyl is being chosen, though. It has a very short duration and would only be good for breakthrough pain management while looking at a longer term solution. The patient would be better served with an equinanalgesic dose of a longer acting pain medication like morphine or hydromorphone.