[coldtea]

>the quantity 1 added to another quantity 1 does not equal the quantity 2

Our universe already fits the description, as there are algebras where that is not the case (similar as we have geometrics where triangle angles add up to > 180 degrees -- in fact geometry calculations on a sphere surface like earth works like that).

There are also probably physical examples where that's not the case (e.g. unlike adding 1+1 apple, adding two bodies of water gives you one unified body of water).

Could it hold even more fundamentally? Sure why not. Our "not being able to conceive it" doesn't mean much regardless to whether it's possible.