Given a récollement $$ \mathbf{D}^0 \underset{\underset{i_R}\leftarrow}{\overset{\overset{i_L}\leftarrow}\to} \mathbf{D} \underset{\underset{q_R}\leftarrow}{\overset{\overset{q_L}\leftarrow}\to} \mathbf{D}^1 $$ the machinery exposed in BBD's Faisceaux Pervers (Astérisque 100), and in a more modern language in

Banagl, Markus. Topological invariants of stratified spaces. Springer Science & Business Media, 2007.

provides one with a $t$-structure on $\mathbf D$ obtained by "gluing par récollement" a $t$-structure $(\mathcal{D}_\ge^0, \mathcal{D}_\le^0)$ on $\mathbf D_0$ and a $t$-structure $(\mathcal{D}_\ge^1, \mathcal{D}_\le^1)$ on $\mathbf D_1$.

[BBD] and Banagl book, starting from the classical geometric example of a stratification $\varnothing\subset U\subset X$ for a topological space, both insist on the fact that

By applying the gluing Theorem [i.e. the construction providing the glued $t$-structure] inductively, the notion of a p-perverse t-structure quickly generalizes to spaces with more than two strata

The possibility of doing this ultimately relies into the fact that gluing par récollement is an associative operation, namely (in some sense to be specified) if we denote the [left aisle of the] glued $t$-structure above as $\mathcal{D}^0_\ge\wr\mathcal{D}_\ge^1$, we have $$ (\mathcal{D}^0_\ge\wr\mathcal{D}_\ge^1)\wr \mathcal{D}^2_\ge = \mathcal{D}^0_\ge\wr(\mathcal{D}_\ge^1\wr \mathcal{D}^2_\ge) $$ In the geometric setting, I expect this result ultimately depend on the commutation of some diagrams of adjoint functors. But

What happens in the general setting of an "abstract" recollement in a generic triangulated (or better, stable) category? Is there any property of recollements ensuring that the glued $t$-structure $\mathcal{D}_0 \wr\dots \wr \mathcal{D}_n$ exists in a definite sense?

Note: this question is motivated by the same interest.