Multiple Narcotics

I have a question for you pain management experts. I am a nursing student in my final year of school and recently had a teenage postop patient with pain control issues. We gave him 2 Tylenol #3s that had no effect (he weighs 100kg) and so the debate began about whether or not he could get IV morphine on top. The orders didn't specify that only 1 could be given each 4 hours. I was wondering if you could safely give the morphine on top of the Tylenol #3s (it was 2 hours after) or would you risk narcotic overdose? The unit nurses couldn't agree and the literature I have been reading is not clarifying things either.