How many items can a player carry at most?

Your inventory has 4 rows of 9 slots each. That is 36 slots, plus one for the right hand, 37 slots. Each one can carry a single (non-stackeble) Shulker Box with up to 3 × 9 slots for items. So one Shulker box can carry up to 3 × 9 × 64 = 1728 items. And if you have 37 Shulker Boxes in your inventory, you get 37 × 1728 = 63936 items. Plus, 4 items armor and 37 shulker boxes, so 63973 items.

In case you count the contents of an Ender Chest a part of your inventory, you get an extra 26 slots plus 27 Shulker Boxes, that is 44955 + 63940 = 108895 items total.

In case you you're willing to count the Ender Chest and carrying iron/gold blocks to craft nuggets (1 block = 81 nuggets), the grand total is 1701 slots * 64 blocks * 81 = 8817984 items, plus the 67 storage items and armour = 8818051 items total! (5104 chests)

One can carry up to 8818051 items at once¹

¹: With commands or other non-vanilla additions, Shulker Boxes can be stacked to 64 - that makes a grand total of 1701 * 64 * 64 * 81 + 4032 boxes + 4 armor = 564355012 items (326594 chests)

37 slots in a player inventory. Lets say we use 36 for shulkerboxes and 1 for an enderchest to add another 27 slots.

so youve got 63 slots total to fill with Shulkerboxes. 63 * 27 (slots in a shulkerbox) = 1701 slots total.

1701 stacks of items! which is 1701 * 64 = 108,864 items total in the shulkerboxes and enderchest on you!

But wait theres more.. lets say if you were carrying Ingots.. you could transform the items into nuggets.. which means..... 108,864 * 9 = 979,776 Nuggets at once.

Now if you want the total ITEMS, you take that number, add the shulkerboxes and enderchest to it, and 4 armor slots (the shulkerboxes and enderchest and armour are items as well) which is a grande total of 979,776 + 27 + 37 + 4 = 979,844 items.

(which is btw 283.5 Double chests full of items! all on you at once!)