Let $\mathfrak{h}$ be a Cartan subalgebra of a $\mathbb{C}$-semi simple Lie algebra $\mathfrak{g}$. Given $\lambda \in \mathfrak{h}^*$, $M(\lambda)$ the Verma module of highest weight $\lambda$ and $N(\lambda)$ its maximal submodule.

1. Do we have examples of $\lambda$ integral and regular for which $N(\lambda)$ is not equal to the sum of the Verma modules it contains?

2. Is there any conditions on $\lambda$ to get 1.?

I know BGG gave an example for $\mathfrak{sl}_4(\mathbb{C})$ but $\lambda=-\omega_1-\omega_3$ is singular.

Thanks.