In this paper, Kuznetsov mentions that the following triangulated categories have the Jordan-Holder properties

• $\mathbf{D}(\Bbb P^1)$ and $\mathbf{D}(\Bbb P^1/\Gamma)$
• connected Calabi-Yau categories
• derived categories of curves of positive genus

These are the only examples of geometric triangulated categories with the Jordan-Holder property that I know of. Are there any others?

In this paper, Kuznetsov mentions that the following triangulated categories have the Jordan-Holder property

• $\mathbf{D}(\Bbb P^1)$ and $\mathbf{D}(\Bbb P^1/\Gamma)$
• connected Calabi-Yau categories
• derived categories of curves of positive genus

These are the only examples of geometric triangulated categories with the Jordan-Holder property that I know of. Are there any others?