Moon shards stack indefinitely, and the maximum attack speed is 1000, so that's

1000 IAS / 55 (IAS per Shard) * 4000 gold = 73,000 gold

Towers can be upgraded 10 times each, and there's 6 towers = 45,000 gold

Barracks can be upgraded 10 times each, with 6 barracks = 45,000 gold

So you can spend 163,000 additional gold on yourself/your base after you've become 6-slotted.

How do you upgrade the base?

There is a new consumable in the store that you use on the buildings to upgrade them.

It's mostly moon shards and building upgrades, as it was already mentioned. But here are a few more ideas.

very personal courier with:
necronomicon
manta
one more item instead of boots of travel (which can be moved to your personal courier)
refresher (depends on a hero)

or even more ideas, but these are just ideas, so I'm not sure:
use active effect of guardian greaves (if none of your team mates has it and you don't want to keep them in your inventory all the time), drum, crimson guard, blade mail, mjollnir, and then move that item back to your personal courier, or idk, keep them on the ground. needs to be fast, yeah, but it's fun!

Good idea.
You can also play Meepo, to spend 4x73,000 gold of moonshards, to max out each Meepo clone.
Or Lone Druid, to stuck up your Spirit bear with additional 6 slots and 73,000 gold of moonshards.
Playing Alchemist is a good idea too, since you also can spend 5x4,200 gold to buy aghs to your teammates.