modules for the current algebra $\mathfrak{sl}_2[t]$ which admit a filtration whose successive quotients are isomorphic to stable Demazure modules. These types of filtrations are called excellent filtrations [@Jo03; @J06] but are also known in the literature as Demazure flags [@BCSV15; @CSSW14]. Demazure modules occur in highest weight integrable modules of the affine Lie algebra $\widehat{\mathfrak{sl}_2}$ and are called stable if they admit an action of the maximal parabolic subalgebra $\mathfrak{sl}_2[t]$; the integer given by the action of the canonical central element is called its level. The great interest in Demazure modules is due to several reasons. They appear as classical limits of a family of irreducible representations of the quantum affine algebra [@BCMo15; @CP01], their graded characters are specializations of Macdonald polynomials [@I03] and satisfy certain functional relations which are known as $Q$–systems [@CV13; @KV14], just to name a few.

An important result due to Naoi states that if $m \geq m' \geq 1$, then a stable Demazure module of level $m'$ admits a filtration such that the successive quotients are isomorphic to level $m$–Demazure modules. In fact Naoi proves this result for an affine Lie algebra associated to a simply laced simple Lie algebra. Later, this result was greatly 