  We consider systems of backward stochastic differential equations with
c\`adl\`ag upper barrier $U$ and oblique reflection from below driven by an
increasing continuous function $H$. Our equations are defined on general
probability spaces with a filtration satisfying merely the usual assumptions of
right continuity and completeness. We assume that the pair $(H(U),U)$ satisfies
a Mokobodzki--type condition. We prove the existence of a solution for
integrable terminal conditions and integrable quasi--monotone generators.
Applications to the optimal switching problem are given.
