What is the maximum PC carrying weight?

Question

My fellow purveyors of fine cheese, I require some assistance in importing some expensive aged cheeses from my home lands. While I would normally call on my Barbarian associate to bring my cheeses across the great sea, he has recently become, how should I say, adverse to ships, and something just seems off about him since he returned from his last adventure...

Anyway, I've come to this marketplace to investigate the acquisition of some new services regarding the transportation of my fine goods. After losing most of my last shipment to the great sea, I require a single individual to physically carry my cheese from it's source to my stall here. However, I can only afford to hire but a single adventurer for this critical task.

As such, I am inquiring regarding the maximum carrying weight a single PC can carry (so that I can plan and distribute my expansive cheese deliveries accordingly).

As a picky merchant, however, I should provide some guidelines for the type of individual I am seeking:

• This individual must be able to physically carry the goods him (or her) self. This is to say that I refuse to use Bags of Holding (I would rather not risk an unfortunate incident), or other supernatural means (teleportation, plane shifting, etc) by which the carrying of the goods would be taken out of this courier's hands (I cannot risk losing this delivery). However, if your courier prefers to swim or fly instead of walking or running, that would be fine by me.
• Your adventurer may be as famous or infamous as you can find (though anyone above level 20 may be beyond what I can afford).
• Nevertheless, as a savvy merchant I do have some strong connections (both legal and er... otherwise), so assume that gold is of no object when it comes to the purveyance of items or other equipment.
• While I do not trust Bags of Holding, other magical items you can find to enhance the carrying capacity of your courier are acceptable (call me old fashioned, but I'd take a well-equipped adventurer carrying my goods over some unseen magical servant any day).
• Any strange creatures or objects currently identified by the Wizards of the Coast are acceptable, though be prepared for additional scrutiny if you use information found in their newest edition of Unearthed Arcana.

There are also some restrictions I should probably outline:

• I simply cannot accept the use of a "Wish" spell - beyond not even knowing if such a thing exists (I've certainly never observed one in my wide travels of these lands), I would prefer to trust my goods with an individual, and not rely solely on magic (after all, I can't risk flooding the market with my fine cheeses).
• The individual I am trusting should not be a god or deity. My business requires me to be discreet about who I deal with, and any semblance of preferential treatment to one deity over others could be disastrous for other aspects of my business.

So friends and fellow cheese aficionados, what is the most a courier can carry?

Answer 1

So, ultimately, we're looking at a way to maximize a PC's strength score, and multiply their carry capacity as many times as possible. This is easy enough.

You need a Goliath, Orc, Bugbear, or Firbolg (all from Volo's Guide) who is an 18th Level Druid. They should be wearing a Belt of Frost Giant Strength and carrying a pile of Potions of Growth.

Those 4 Races have the following Feature:

Powerful Build: You count as one size larger when determining your carrying capacity and the weight you can push, drag, or lift.

Our 18th Level Druid should shapeshift into a Mammoth. A Mammoth has a Strength of 24, and is Huge. By default, this gives the Mammoth a carry capacity of 1,440 lbs.

Now, because Wild Shape specifies that

You retain the benefit of any features from your class, race, or other source and can use them if your new form is physically capable of doing so.

It seems that Powerful Build still applies while Wild Shaped. So, our Mammoth counts as Gargantuan for determining carry capacity. This takes us up to 2,880 lbs.

Now, the spell Enhance Ability has a Material Component, so the Druid cannot cast this spell while Wild Shaped. But, shapeshifting doesn't break concentration on the spell. So the Druid can cast the spell on themselves as Bull's Strength, then shapeshift, and grab their load. This doubles our carry capacity again, taking us up to 5760 lbs.

Next up is a bit of a conundrum. Normally, I'd suggest using a Potion of Growth to increase your Size Category...but you already count as Gargantuan for determining your carry capacity...and per RAW, there are no sizes in 5E that are larger than this. So we'll skip that one for the moment (don't worry, we'll come back to it).

Because we're dealing with a Mammoth here, and given the sheer volume of cheese we are moving, I'd suggest using a Cart. This lets us use the Mammoth's Pulling capacity, taking it up to 11,520 lbs.

But wait, there's more! Wild Shape also specifies this:

You choose whether your equipment falls to the ground in your space, merges into your new form, or is worn by it. [...] Equipment that merges with the form has no effect until you leave the form.

When you shapeshift...anything you are carrying is basically gone...merged into your form having 'no effect.' This is generally interpreted to mean that they also have no weight while you are shapeshifted.

So...our Druid should pick up as much cheese as possible before they shapeshift.

Our Druid is wearing a Belt of Frost Giant Strength and has cast Enhance Ability on themselves. This gives them a strength of 29, doubled carry capacity, and they count as Large for determining their capacity. So they can carry 1,740 lbs. Chug that Potion of Growth now, and become Size Large, counting at Size Huge...and double your capacity again: 3,480 lbs.

So, our Druid will cast Enhance Ability on themselves, knock back a Potion of Growth if they need it, then pick up 3,480 lbs of Cheese, then immediately Shapeshift into a Mammoth and hook into a Wagon loaded with 11,520 lbs of Cheese. Giving us a total cargo capacity of 15,000 lbs of Cheese.

They'll need to stop once an hour to refresh the spell on themselves, and will need a Short Rest every 2 hours to reset their uses of Wild Shape (get a 20th level Druid if you don't want that break every 2 hours). But they shouldn't have any problem meeting the standard 8 hours per day of travel time.

(Note: If your DM rules that the Colossal size category exists, then the effect of the Potion of Growth on your Mammoth form will apply, doubling your drag capacity yet again).

Addendum: If you don't trust Shapeshifters...and letting them magically absorb your Cheese, then get yourself a Multiclassed Barbarian 6/Sorcerer 5. The Barbarian should be a Totem Warrior, and have taken the Bear Totem feature at 6th level. The Sorcerer should have the Extended Spell Metamagic. Otherwise, keep race and magic item collection the same. This caps you at 13,920 lbs pulled in a cart.

Answer 2

Well, simply put... WE CAN CARRY MORE CHEESE THAN THAT PEOPLE! Let's assume this is a level 14 Rune Knight with access to magic items, preferably a Giff rune knight (recent UA) Said Giff rune knight is using a belt of storm giant strength, combined with a hammer of thunderbolts, also wearing some Gauntlets of Ogre power (not attuned) granting them 30 strength (the RAW maximum, god level) This allows them to count as huge for carry weight, and with a simple calculation (30 times 6 times 15) this grants them a pretty high carry weight of 2700 pounds.

From here the answer is to grant them a couple more magic items. a few spell wrought tattoo's, filled with the Enhance Ability spell and A potion of growth this grants them a significantly higher carry weight than before, (30 times 8 times 15 times 2 which is) 7200 pounds.

if you're really savvy, we can do away with all of that, and simply use a glory paladin, with at least 6 levels in totem barbarian (6th level bear), and the rest in cleric if you want for extra channel divinity uses.

With some potions of speed (for speedy travel, gotta get those cheeses)

Potions of giant size, for huge size

potions of growth, for gargantuan size after that

spell-wrought tattoos as mentioned above

and finally, that same belt of storm giant strength, combined with a hammer of thunderbolts, with some Gauntlets of Ogre power (not attuned).

This grants our very buff boi (or girl) a carry weight of (30 times 2 times 2 times 8 times 15 which equals) 14400 pounds of cheese. MAXIMUM CHEESE!

Answer 3

Find yourself a copy of the Manual of Gainful Exercise, then throw your cheese mule character into a hyperbolic time chamber type of thing so that they can read the manual multiple times - resurrect them if they die.
Technically you could repeat this process infinitely for unholy cheese toting results, but considering the 1 year in the chamber to 1 day on earth thing, if you leave him in there for 2 years he has 7 uses of the manual.
That would be +14 to his strength score, +7 to modifier. If he started with a 16 he's got a 30 strength now.
Slap a storm giant belt on and he can carry your entire stock on one finger, and that's not to mention if you do this to a goliath carrying capacity build.