There isn't a cap technically but, Rammus is the only one who can reach it. you have to stack 6 Thornmails, have only armor runes and use the armor increasing mastery. Works great until you come along a team of casters.
There's no cap. There is, however, a current technical highest possible amount you can get to. As you said, Rammus with DBC, 6 Thornmails, all scaling armor runes, armor mastery, on a team with a Taric holding Aegis, a Sona playing Aria of Perseverance, and a Soraka who blesses him to increase armor.





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Perfect setup for armor "cap":
Soraka using Astral Blessing on master Yi.
Galio using Bulwark on Master Yi.
Master Yi using Meditate and stacking 6 Thornmails.
Taric standing by with Shatter aura and Aegis of the Legion.
Mordekaiser using Creeping Death on Master Yi.
Master Yi now has the highest armor, ever!
Soraka using Astral Blessing on master Yi.
Galio using Bulwark on Master Yi.
Master Yi using Meditate and stacking 6 Thornmails.
Taric standing by with Shatter aura and Aegis of the Legion.
Mordekaiser using Creeping Death on Master Yi.
Master Yi now has the highest armor, ever!

Aren't we forgetting Malphite's
Brutal Strikes? It increases his armor by 40%. That can be a pretty hefty amount with 6thornmails and a lot of buffs.

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Jebus McAzn wrote:
This thread is now about the highest possible armor you can reach on any champ. Screw MR.
There's not enough MR increasing skills/items to make it worthwhile.

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curious, thanks