There's nothing preventing you from doing so, but there hasn't ever needed to be because barring an extremely niche addition like this, there's virtually no benefit for doing so. I wasn't quoting the rules for an armored coat (seriously, I hadn't even looked at it), I was quoting the core rules in the way stacking works.
In other words, sure, you can put on more and more armor, but it's only going to hurt you most of the time. Armor is one of the heaviest things that you can wear. Even a chain shirt is 20 lbs. Since armor bonuses do not stack but instead overlap, and you take the worst of the penalties for the same reason, and take the worst of the speed reductions for the same reason, but still have to track the weight of both of them, you're just ruining your encumbrance.
The only upside I can think of for this sort of thing would be to get a sort of sunder-resistance going on. However, that's not even a great idea either since armor tends to become really sunder resistant anyways (+5 mithral full plate has a hardness of 25 and 95 Hp) and enhancing multiple suits of armor is costly.