  Let $M$ be a manifold equipped (locally) with a pair of complementary
foliations. In Catuogno, da Silva and Ruffino (Stoch. Dyn. 2013), it is shown
that, up to a stopping time $\tau$, a stochastic flow of local diffeomorphisms
$\varphi_t$ in $M$ can be decomposed in diffeomorphisms that preserves this
foliations. In this article we present techniques which allows us to extend the
time of this decomposition. For this extension, we use two techniques: In the
first one, assuming that the vector fields of the system commute with each
other, we apply Marcus equation to jump nondecomposable diffeomorphisms. The
second approach deals with the general case: we introduce a `stop and go'
technique that allows us to construct a process that follows the original flow
in the `good zones' for the decomposition, and remains paused in `bad zones'.
Among other applications, our results open the possibility of studying the
asymptotic behaviour of each component. \end{abstract}
