The maximum is 3600mg per day.
I am currently between 2400mg and 2700mg (divided over three doses each day).
2700 definitely works for me, but 2400 is marginal (but I take too many pills as it is).
The big trick seems to be to spread these doses out over the day.
If you take them too close together, you can end up with a gap where there is none in your system - and along comes the pain.
Try to get an 8-hour spacing between doses if possible.
I got this wrong a few months back. An early night and a lie-in had me with the whole left side/arm/leg in pain.
A quick grab for the morning dose (without waiting for breakfast) had the pain relieved in less than an hour.
A nice thing about Gabapentin is that you can take it without food.
There are stronger painkillers (like Pregabalin) if the maximum dose does not work - but I do not like the look of the side effects.
Of course, that day may yet come …