ct.category theory – What is the largest subcategory C of a module category over an Artin algebra, such that C is Krull-Schmidt (and albelian)? Does C exist?

Let $A$ be an Artin algebra, $text{Mod},A$ the category of $A$-modules and $text{mod},A$ the category of finitely generated $A$-modules. It is well-known that $text{mod},A$ is a Krull-Schmidt category. Can we find a larger full subcategory $mathcal{C}$ of $text{Mod},A$, such that it remains a Krull-Schmidt category? Is there a largest $mathcal{C}$ and if yes, how does $mathcal{C}$ look like? What happens if we additionally demand $mathcal{C}$ to be an albelian category?