The space you’re looking for is occupied by magic items.
This doesn’t really exist for mundane armors. Without magic items, your AC is determined by your armor, and whether or not you are wearing a shield, and that is all. Mundane armor is a “just pick one and move on” sort of exercise. There is no going to the blacksmith to upgrade your pauldrons or to add steel gauntlets to your leather kit.
What 5e does have are magic items of various kinds that provide a bonus to your AC. There are several magic items that you can wear in addition to your standard armor that provide a bonus to your AC, such as the ring and cloak of protection, or the watchful helm. And of course, there are also +X versions of most mundane armors that provide some bonus to AC. Whether or not these items are common, rare, or in your game at all is up to your DM.
And because this space is reserved for magic items, implementing this sort of system where AC bonuses are cheap and easy to acquire is inherently unbalanced. I elaborate on this in my answer to a similar question about stacking different armors for AC benefits (Can a character wear both chain mail and leather armor to get a higher AC?):
If a ruling trivializes magic items that cost thousands of gold, the ruling is suspect.
First, I must mention that Bardic Wizard's answer is exactly correct, so I won't be repeating the rules here - just read and upvote their answer for that. However, I do want to approach this from another direction by applying an interpretation principle that I have found quite useful as I read the rules and make rulings.
The idea is this: does this ruling make something else in the game entirely pointless?
With this question, it absolutely does. Chain Mail gives an Armor Class of 16 and costs 75 gp. Leather armor costs 10 gp. This question is really asking something like "Can I get Chain Mail +1 for 85 gp?" And the answer to that question should be obvious: of course not. +1 Armor is classified as "Rare", and going by the Magic Item Rarity table in the Dungeon Master's Guide has a value of 500 gp on the low end, up to 5000 gp on the high end. If wearing some cheap leathers under your chain shirt were just as good as enchanted armor that fetches thousands of gold at the market, there is no point to having magic armor at all.
The space you’re looking for is already filled with magic items, and implementing cheap and easily accessible boosts to AC trivializes those magic items, which is wrong, it’s just something to be aware of should you choose to do so in your games. There is a reason AC bonuses are very expensive: they’re deceptively powerful.