I know people with permanent pain due to medical conditions who have been given a doctor's approval to exceed the limits printed on the packaging (after having previously been monitored). You can exceed the limit on the packaging by one or two pills.
A bit more is often not deadly, but it's very easy to take more than a bit. When I had a messed up mouth for several days, I took the maximum doses and set timers to help me regulate the dosage throughout the day, but I sure wished I could've taken more at that time.
From personal experience if i have a headache I'll take 1000 mg all at once; it either works right away or it doesnt and I stop bothering until I've had a good nights rest...
I had only very brief experiences with longer intense pain but it made my mind into pudding and desperate knot of how-to-stop-this-at-all-costs. Normal life is not possible and sanity is not granted.