Assuming you max out the respective Armor Perks (+100% Armor, +25% for a full set, +25% for all same type), max out Smithing and then use Alchemy/Enchanting loop, you can make ANY Armor set reach the Armor cap. Upgrading works by adding a flat value to your items and has nothing to do with base values.
If you're wondering what the Alchemy/Enchanting loop is, it works like this: You max out all three Crafting Skills. Then you make a potion that boosts Enchanting. Drink that potion and enchant a set of gear that boosts Alchemy. Put that gear on and make another potion that boosts Enchanting. Since all crafting skills benefit from going over 100, you can keep this loop going for a while. It has diminishing returns, though, so at some point you'll want to stop and use your hyperboosted Alchemy to craft Smithing enhancing potions and your hyperboosted Enchanting to enchant a set of Smithing boosting gear. Now, with your utterly ridiculous Smithing level, you can make anything reach the Armor cap and upgrade weapons to ridiculous amounts (one shotting Ancient Dragons isn't out of the question).
That being said, you might not need to go to such insane levels. Just maxing out Smithing (and the respective Armor Perk tree) can bring most item sets to the max cap. I don't have the exact numbers, but I'm pretty sure most Heavy Armor sets don't need the loop to hit the cap, and neither do most Light Armor sets. The loop is mostly used to make your weapons godlike, since there's no cap there...