  Given a reference filtration $\mathbb{F}$, we develop in this work a generic
method for computing the semimartingale decomposition of
$\mathbb{F}$-martingales in some specific enlargements of $\mathbb{F}$. This
method is then applied to the study of progressive enlargement with multiple
non-ordered random times, for which explicit decompositions can be obtained
under the absolute continuity condition of Jacod.
