- Endurance - 15
- Power - 18
- Frenzy - 17
A quick note: To reach the maximum of a specific charge type, I'm assuming you're using two Precursor's emblem with +3 to the charge type you're trying to maximize.
Getting all required items to maximize the charges is extremely unlikely but it is possible in theory.
All charges (12 charges)
Per default you can have 3 charges of any type.
Every class can get +3 to maximum for each of the charge types from the skill tree.
Getting the required nodes isn't a problem in terms of skill-points but the viability of it is another topic (although that's part of not the question).
With two extremely well rolled Precursor's Emblem you'll get an additional maximum + 6 to each charge aswell.
Endurance (3 additional charges):
For classes you'll need to be either a Juggernaut or a Chieftain to get +1.
Deaths door is the only specific slot item that will give you +1 to endurance charges.
Apart from that you'll need a lucky Shaper roll on a 2 handed weapon to increase it by +1.
Power (6 additional charges):
To get an additional +1 you'll have to ascend as either an Assassin, Trickster or Occultist.
You will be able to get a whopping +4 power charges from uniques with the following items:
Additionally if you're lucky with a Vaal Orb or corrupted drop you may find a +1 on a helmet slot.
Frenzy (4 additional charges):
As @A_S00 pointed out in his comment you can achieve a total of 17 charges if you're using the Badge of the Brotherhood.
Otherwise the following options are available.
In terms of ascendencies, here you'll have to be either a Trickster or Raider for a +1.
The only unique item that will give you additional charges are the Darkray Vectors (+1).
For modifiers on yellow items you can either get lucky with a corrupted roll on gloves or with a shaper roll on a two-handed weapon (+1 each)